Alexander Schwarz

Dr.-Ing. Alexander Schwarz

Research » Teaching » Career » Supervised theses » Publications

Research

Development of mixed finite element formulations for

  • the incompressible Navier-Stokes equations
  • isotropic und anisotropic hyperelasticity
  • elasto-(visco)plastic material behaviour at finite strains
  • time-dependent problems
  • fluid-structure-interaction (FSI)
  • theory of porous media (TPM)

Teaching

  • Technische Mechanik 1 (Engineering Mechanics 1: Statics / Elastostatics I)
  • Technische Mechanik 2 (Engineering Mechanics 2: Elastostatics II / Hydromechanics)
  • Technische Mechanik 3 (Engineering Mechanics 3: Dynamics)
  • Bauinformatik (Computer Sciences for Civil Engineers)
  • Finite Element Method: Foundations
  • Nonlinear Finite Element Method
  • Computational Inelasticity
  • Multiphase materials
  • Höhere Mechanik (Advanced Mechanics)

Career

1995 High-school diploma (Abitur), Hohenlohe Gymnasium Öhringen
1995- 1996 Civilian service
1996- 2004 Engineering studies (civil engineering), University of Duisburg-Essen and University of Adelaide
2004 Stipendiary of Deutschen Akademischen Austausch Dienst (DAAD)
2004 Diploma thesis at University of Adelaide, Australia, School of Mechanical Engineering. Title: "Investigations to Second Order Derivatives within Meshfree Approximations"
2005- 2009 Research assistant, Institute of Mechanics, Faculty of Engineering, Department Civil Engineering, University of Duisburg-Essen
2009 Doctoral degree (Dr.-Ing.), University Duisburg Essen, Title: "Least- Squares Mixed Finite Elements for Solid Mechanics"
2010 "Akademischer Rat", Institute of Mechanics, University Duisburg- Essen
2011 Director of the international master degree course Computational Mechanics
2013 Academic senior councilor at the Institute of Mechanics, University Duisburg- Essen

Supervised theses

  • Kugai, S. [2017], "Investigation of mixed least-squares finite element formulations for the incompressible Navier-Stokes equations based on quadrilateral and hexahedral elements.", Master thesis, Institut of Mechanics, Dept. of civil engineering, University Duisburg-Essen.
     
  • Levermann, J. [2016], "Investigation of Newmark time integration schemes for the incompressible Navier-Stokes fluid flow in least-squares finite element methods.", Master thesis, Institut of Mechanics, Dept. of civil engineering, University Duisburg-Essen.
     
  • Endrikat, L. [2016], " Mixed Galerkin finite element method in 2D und 3D for the incompressible Navier-Stokes equations.", Master thesis, Institut of Mechanics, Dept. of civil engineering, University Duisburg-Essen.
     
  • Depenbrock, R. [2016], " On a three- dimensional mixed least-squares finite element formulation interpolating stresses and displacements in H$^1$($\mathcal{B}$) under consideration of small strains.", Master thesis, Institut of Mechanics, Dept. of civil engineering, University Duisburg-Essen.
     
  • Averweg, S.  [2016], "Least-squares FEM with Lagrange interpolation in 2D and 3D for the S-V-P formulation of the incompressible Navier-Stokes equations. ", Master thesis, Institut of Mechanics, Dept. of civil engineering, University Duisburg-Essen.
     
  • Maassen, S. [2016], "On a geometrically nonlinear least-squares finite element formulation for numerical simulations of piezoelectrical coupling phenomenons. ", Master thesis, Institut of Mechanics, Dept. of civil engineering, University Duisburg-Essen.
     
  • Umar, O. [2015], "Mixed Galerkin finite element formulation for the incompressible Stokes/Navier-Stokes equation for newtonian - and non newtonian fluids.", Master thesis, Institut of Mechanics, Dept. of civil engineering, University Duisburg-Essen.
  • Igelbüscher, M. [2015], Comparsion of geometrically lienar and nonlinear finite element formulations of elasto-plasticity.", Master thesis, Institut of Mechanics, Dept. of civil engineering, University Duisburg-Essen.
  • Bohne, F. [2015], "A velocity-vorticity-pressure least-squares finite element formulation of stationary and instationary laminar newtonian fluid flows.", Master thesis, Institut of Mechanics, Dept. of civil engineering, University Duisburg-Essen.
  • Stenchlik, D. [2015], "Implementation and comparsion of mixed least-squares finite elements for the solution of dynamic problems in incompressible linear elasticity.", Bachelor thesis, Institut of Mechanics, Dept. of civil engineering, University Duisburg-Essen.
  • Kugai, S. [2015], "Implementierung und Vergleich der Galerkin und Least-Squares FEM anhand von Transportgleichungen.", Bachelor thesis, Institut of Mechanics, Dept. of civil engineering, University Duisburg-Essen.
  • Averweg, S. [2014], "Comparsion and implementation of least-squares and Kriging approximation approaches.", Bachelor thesis, Institut of Mechanics, Dept. of civil engineering, University Duisburg-Essen.
  • Endrikat, L. [2014], "Implementation and investigation of hexahedral finite elements of different polynomial order.", Bachelor thesis, Institut of Mechanics, Dept. of civil engineering, University Duisburg-Essen.
  • Viebahn, N. [2014], "Implementation of higher order finite elementr for quasi-incompressible (non-) linear elasticity in AceGen.", Master thesis, Institut of Mechanics, Dept. of civil engineering, University Duisburg-Essen.
  • Nisters, C. [2013], "Mixed finite element implementation of a two-dimensional strain gradient elasticity model", Master thesis, Institut of Mechancs, Dept. of civil engineering, University Duisburg-Essen.
  • Serdas, S. [2012], "Comparison of stabilization techniques for mixed Galerkin FEM in the field of transport and flow problems.", Master thesis, Institut of Mechanics, Dept. of civil engineering, University Duisburg-Essen.
  • Romanski, L. [2011], "Konstruktion und Implementierung von skalar- und vektorwertigen Ansatzfunktionen höherer Ordnung", Bachelor thesis, Institut of Mechanics, Dept. of civil engineering, University Duisburg-Essen.
  • Saubke, V. [2011], "Numerische Untersuchungen von Viereckselementen für konforme Diskretisierungen in H(div) ", Bachelor thesis, Institut of Mechanics, Dept. of civil engineering, University Duisburg-Essen.
  • Steeger, K. [2010], "A weighted mixed Least-Squares finite element formulation solving linear elastodynamic problems", Master thesis, Institut of Mechanics, Dept. of civil engineering, University Duisburg-Essen.
  • Steeger, K. [2008], "A least-squares mixed finite element formulation based on the St. Venant-Kirchhoff material law", Bachelor thesis, Institut of Mechanics, Dept. of civil engineering, University Duisburg-Essen.
  • Kampen, A. [2007], "Gemischte Least-Squares Finite Elemente für lineare, inkompressible Elastizität", Diploma thesis, Institut of Mechanics, Dept. of civil engineering, University Duisburg-Essen.
  • Bujna, G. [2006], "Berechnung von Raumluftströmungen - Konvergenzstudien strömungsmechanischer Probleme mit dem Programmsystem FLUENT", Diploma thesis, Institut of Mechanics, Dept. of civil engineering, University Duisburg-Essen.

Publications

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Schwarz A, Bluhm J and Schröder J (accepted (2019)), "A finite element formulation for freezing and thawing processes of ice within the framework of the TPM", In Research and Applications in Structural Engineering, Mechanics & Computation. Cape Town, South Africa Taylor & Francis Group.

[BibTeX]
BibTeX: 
@incollection{SchBluSch:2019:afe,
  author = {J. Schröder and J. Bluhm and A. Schwarz},
  editor = {A. Zingoni},
  title = {A finite element formulation for freezing and thawing processes of ice within the framework of the TPM},
  booktitle = {Research and Applications in Structural Engineering, Mechanics & Computation},
  publisher = {Taylor & Francis Group},
  year = {2019}
}
Averweg S, Schwarz A, Nisters C and Schröder J (2018), "Implicit time discretization schemes for least-squares finite element formulations to model incompressible flows", Proceedings in Applied Mathematics and Mechanics. Vol. 18, pp. e201800166 (2 pages).

[BibTeX]
BibTeX: 
@article{AveSchNisSch:2018:itd,
  author = {S. Averweg and A. Schwarz and C. Nisters and J. Schröder},
  title = {Implicit time discretization schemes for least-squares finite element formulations to model incompressible flows},
  journal = {Proceedings in Applied Mathematics and Mechanics},
  year = {2018},
  volume = {18},
  pages = {e201800166 (2 pages)}
}
Igelbüscher M, Schwarz A, Steeger K and Schröder J (2018), "Modified mixed least-squares finite element formulations for small and finite strain plasticity", International Journal for Numerical Methods in Engineering. Vol. 117, pp. 141-160.

[BibTeX]
BibTeX: 
@article{IgeSchSteSch:2018:mml,
  author = {Igelbüscher, M. and Schwarz, A. and Steeger, K. and Schröder, J.},
  title = {Modified mixed least-squares finite element formulations for small and finite strain plasticity},
  journal = {International Journal for Numerical Methods in Engineering},
  year = {2018},
  volume = {117},
  pages = {141--160}
}
Nisters C and Schwarz A (2018), "Efficient stress--velocity least-squares finite element formulations for the incompressible Navier--Stokes equations", Computer Methods in Applied Mechanics and Engineering. Vol. 341, pp. 333 - 359.

[BibTeX]
BibTeX: 
@article{NisSch:2018:esv,
  author = {C. Nisters and A. Schwarz},
  title = {Efficient stress--velocity least-squares finite element formulations for the incompressible Navier--Stokes equations},
  journal = {Computer Methods in Applied Mechanics and Engineering},
  year = {2018},
  volume = {341},
  pages = {333 - 359}
}
Nisters C, Schwarz A, Averweg S and Schröder J (2018), "Remarks on a Fluid-Structure Interaction Scheme Based on the Least-Squares Finite Element Method at Small Strains", In Advances in Mechanics of Materials and Structural Analysis: In Honor of Reinhold Kienzler. , pp. 261-279. Springer International Publishing.

[BibTeX]
BibTeX: 
@incollection{NisSchAverSch:2017:roa,
  author = {Nisters, Carina and Schwarz, Alexander and Averweg, Solveigh and Schröder, Jörg},
  editor = {Altenbach, Holm and Jablonski, Frank and Müller, Wolfgang H. and Naumenko, Konstantin and Schneider, Patrick},
  title = {Remarks on a Fluid-Structure Interaction Scheme Based on the Least-Squares Finite Element Method at Small Strains},
  booktitle = {Advances in Mechanics of Materials and Structural Analysis: In Honor of Reinhold Kienzler},
  publisher = {Springer International Publishing},
  year = {2018},
  pages = {261--279}
}
Schwarz A, Averweg S, Nisters C and Schröder J (2018), "A fluid-structure interaction approach with inherently fulfilled coupling conditions", Proceedings in Applied Mathematics and Mechanics. Vol. 18, pp. e201800183 (2 pages).

[BibTeX]
BibTeX: 
@article{SchAveNisSch:2018:afs,
  author = {A. Schwarz and S. Averweg and and C. Nisters and J. Schröder},
  title = {A fluid-structure interaction approach with inherently fulfilled coupling conditions},
  journal = {Proceedings in Applied Mathematics and Mechanics},
  year = {2018},
  volume = {18},
  pages = {e201800183 (2 pages)}
}
Schwarz A and Dwight R (2018), "Data Assimilation for Navier-Stokes using the Least-Squares Finite-Element Method", International Journal for Uncertainty Quantification. Vol. 8(5), pp. 383-403.

[BibTeX]
BibTeX: 
@article{SchDwi:2018:daf,
  author = {Schwarz, A. and Dwight, R.},
  title = {Data Assimilation for Navier-Stokes using the Least-Squares Finite-Element Method},
  journal = {International Journal for Uncertainty Quantification},
  year = {2018},
  volume = {8},
  number = {5},
  pages = {383--403}
}
Schwarz A, Nickaeen M, Serdas S, Nisters C, Ouazzi A, Schröder J and Turek S (2018), "A comparative study of mixed least-squares FEMs for the incompressible Navier-Stokes equations", International Journal of Computational Science and Engineering. Vol. 17(1), pp. 80-97.

[BibTeX]
BibTeX: 
@article{SchNicSerNisOuaSchTur:2018:acs,
  author = {A. Schwarz and M. Nickaeen and S. Serdas and Carina Nisters and A. Ouazzi and J. Schröder and S. Turek},
  title = {A comparative study of mixed least-squares FEMs for the incompressible Navier-Stokes equations},
  journal = {International Journal of Computational Science and Engineering},
  year = {2018},
  volume = {17},
  number = {1},
  pages = {80--97}
}
Schwarz A, Nisters C, Averweg S and Schröder J (2018), "Stress-Velocity Mixed Least-Squares FEMs for the Time-Dependent Incompressible Navier-Stokes Equations", In Large-Scale Scientific Computing. Cham , pp. 137-144. Springer International Publishing.

[BibTeX]
BibTeX: 
@inproceedings{SchNisAveSch:2017:svm,
  author = {Schwarz, Alexander and Nisters, Carina and Averweg, Solveigh and Schröder, Jörg},
  editor = {Lirkov, Ivan and Margenov, Svetozar},
  title = {Stress-Velocity Mixed Least-Squares FEMs for the Time-Dependent Incompressible Navier-Stokes Equations},
  booktitle = {Large-Scale Scientific Computing},
  publisher = {Springer International Publishing},
  year = {2018},
  pages = {137--144}
}
Schwarz A, Steeger K, Igelbüscher M and Schröder J (2018), "Different approaches for mixed LSFEMs in hyperelasticity: Application of logarithmic deformation measures", International Journal for Numerical Methods in Engineering. Vol. 115, pp. 1138-1153.

[BibTeX]
BibTeX: 
@article{SchSteIgeSch:2018:daf,
  author = {Schwarz, A. and Steeger, K. and Igelbüscher, M. and Schröder, J.},
  title = {Different approaches for mixed LSFEMs in hyperelasticity: Application of logarithmic deformation measures},
  journal = {International Journal for Numerical Methods in Engineering},
  year = {2018},
  volume = {115},
  pages = {1138--1153}
}
Igelbüscher M, Schwarz A, Steeger K and Schröder J (2017), "Remarks on a modified mixed least-squares finite element formulation for small strain elasto-plasticity", Proceedings in Applied Mathematics and Mechanics. Vol. 17, pp. 311-312.

[BibTeX]
BibTeX: 
@article{IgeSchSteSch:2017:roa,
  author = {Igelbüscher, M. and Schwarz, A. and Steeger, K. and Schröder, J.},
  title = {Remarks on a modified mixed least-squares finite element formulation for small strain elasto-plasticity},
  journal = {Proceedings in Applied Mathematics and Mechanics},
  year = {2017},
  volume = {17},
  pages = {311--312}
}
Nisters C, Schwarz A and Schröder J (2017), "Investigation of stress-velocity LSFEMs for the incompressible Navier-Stokes equations", Proceedings in Applied Mathematics and Mechanics. Vol. 17, pp. 631-632.

[BibTeX]
BibTeX: 
@article{NisSchSch:2017:ios,
  author = {C. Nisters and A. Schwarz and J. Schröder},
  title = {Investigation of stress-velocity LSFEMs for the incompressible Navier-Stokes equations},
  journal = {Proceedings in Applied Mathematics and Mechanics},
  year = {2017},
  volume = {17},
  pages = {631--632}
}
Schröder J, Igelbüscher M, Schwarz A and Starke G (2017), "A Prange-Hellinger-Reissner type finite element formulation for small strain elasto-plasticity", Computer Methods in Applied Mechanics and Engineering. Vol. 317, pp. 400-418.

[BibTeX]
BibTeX: 
@article{SchIgeSchSta:2016:aph,
  author = {J. Schröder and M. Igelbüscher and A. Schwarz and G. Starke},
  title = {A Prange-Hellinger-Reissner type finite element formulation for small strain elasto-plasticity},
  journal = {Computer Methods in Applied Mechanics and Engineering},
  year = {2017},
  volume = {317},
  pages = {400--418}
}
Igelbüscher M, Schröder J and Schwarz A (2016), "On the performance of the Prange-Hellinger-Reissner finite element formulation for elasto-plasticity at small strains", Proceedings in Applied Mathematics and Mechanics. Vol. 16, pp. 203-204.

[BibTeX]
BibTeX: 
@article{IgeSchSch:16:otp,
  author = {M. Igelbüscher and J. Schröder and A. Schwarz},
  title = {On the performance of the Prange-Hellinger-Reissner finite element formulation for elasto-plasticity at small strains},
  journal = {Proceedings in Applied Mathematics and Mechanics},
  year = {2016},
  volume = {16},
  pages = {203-204}
}
Schwarz A, Steeger K, Igelbüscher M and Schröder J (2016), "Comparison of different least-squares mixed finite element formulations for hyperelasticity", Proceedings in Applied Mathematics and Mechanics. Vol. 16, pp. 239-240.

[BibTeX]
BibTeX: 
@article{SchSteIgeSch:16:cod,
  author = {A. Schwarz and K. Steeger and M. Igelbüscher and J. Schröder},
  title = {Comparison of different least-squares mixed finite element formulations for hyperelasticity},
  journal = {Proceedings in Applied Mathematics and Mechanics},
  year = {2016},
  volume = {16},
  pages = {239-240}
}
Schröder J, Turek S and Schwarz A (2016), "Alles im Fluss -- Simulationstechniken der Strömungsmechanik in der Materials Chain", In Essener Unikate 48: Materials Chain -- Forschung aus dem UA Ruhr-Profilschwerpunkt. Universität Duisburg--Essen.

[BibTeX]
BibTeX: 
@incollection{SchTurSch:2016:aif,
  author = {J. Schröder and S. Turek and A. Schwarz},
  title = {Alles im Fluss -- Simulationstechniken der Strömungsmechanik in der Materials Chain},
  booktitle = {Essener Unikate 48: Materials Chain -- Forschung aus dem UA Ruhr-Profilschwerpunkt},
  publisher = {Universität Duisburg--Essen},
  year = {2016}
}
Nisters C, Schwarz A, Steeger K and Schröder J (2015), "A stress-velocity least-squares mixed finite element formulation for incompressible elastodynamics", Proceedings in Applied Mathematics and Mechanics. Vol. 15(1), pp. 217-218.

[BibTeX]
BibTeX: 
@article{NisSchSteSch:2015:asv,
  author = {C. Nisters and A. Schwarz and K. Steeger and J. Schröder},
  title = {A stress-velocity least-squares mixed finite element formulation for incompressible elastodynamics},
  journal = {Proceedings in Applied Mathematics and Mechanics},
  year = {2015},
  volume = {15},
  number = {1},
  pages = {217--218}
}
Schwarz A, Steeger K and Schröder J (2015), "Weighted overconstrained least-squares mixed finite elements for hyperelasticity", Proceedings in Applied Mathematics and Mechanics. Vol. 15, pp. 227-228.

[BibTeX]
BibTeX: 
@article{SchSteSch:2015:wol,
  author = {A. Schwarz and K. Steeger and J. Schröder},
  title = {Weighted overconstrained least-squares mixed finite elements for hyperelasticity},
  journal = {Proceedings in Applied Mathematics and Mechanics},
  year = {2015},
  volume = {15},
  pages = {227--228}
}
Steeger K, Schröder J and Schwarz A (2015), "Comparison of a mixed least-squares formulation using different approximation spaces", Proceedings in Applied Mathematics and Mechanics. Vol. 15, pp. 233-234.

[BibTeX]
BibTeX: 
@article{SteSchSchStaMue:2014:coa,
  author = {K. Steeger and J. Schröder and A. Schwarz},
  title = {Comparison of a mixed least-squares formulation using different approximation spaces},
  journal = {Proceedings in Applied Mathematics and Mechanics},
  year = {2015},
  volume = {15},
  pages = {233--234}
}
Müller B, Starke G, Schwarz A and Schröder J (2014), "A first-order system least squares method for hyperelasticity", SIAM Journal on Scientific Computing. Vol. 36, pp. 795-816.

[BibTeX]
BibTeX: 
@article{MueStaSchSch:2014:afo,
  author = {B. Müller and G. Starke and A. Schwarz and J. Schröder},
  title = {A first-order system least squares method for hyperelasticity},
  journal = {SIAM Journal on Scientific Computing},
  year = {2014},
  volume = {36},
  pages = {795--816}
}
Schwarz A, Steeger K and Schröder J (2014), "Weighted overconstrained least-squares mixed finite elements for static and dynamic problems in quasi-incompressible elasticity", Computational Mechanics. Vol. 54(1), pp. 603-612.

[BibTeX]
BibTeX: 
@article{SchSteSch:2014:wol,
  author = {A. Schwarz and K. Steeger and J. Schröder},
  title = {Weighted overconstrained least-squares mixed finite elements for static and dynamic problems in quasi-incompressible elasticity},
  journal = {Computational Mechanics},
  year = {2014},
  volume = {54},
  number = {1},
  pages = {603--612}
}
Schwarz A, Steeger K, Schröder J, Starke G and Müller B (2014), "An improved mixed finite element based on a modified least-squares formulation for hyperelasticity", Proceedings in Applied Mathematics and Mechanics. Vol. 14, pp. 243-244.

[BibTeX]
BibTeX: 
@article{SchSteSchStaMue:2014:aim,
  author = {A. Schwarz and K. Steeger and J. Schröder and G. Starke and B. Müller},
  title = {An improved mixed finite element based on a modified least-squares formulation for hyperelasticity},
  journal = {Proceedings in Applied Mathematics and Mechanics},
  year = {2014},
  volume = {14},
  pages = {243--244}
}
Serdas S, Schwarz A, Schröder J, Turek S, Ouazzi A and Nickaeen M (2014), "Least-squares finite element methods for the Navier-Stokes equations for generalized Newtonian fluids", Proceedings in Applied Mathematics and Mechanics. Vol. 14, pp. 623-624.

[BibTeX]
BibTeX: 
@article{SerSchSchTurOuaNic:2014:aim,
  author = {S. Serdas and A. Schwarz and J. Schröder and S. Turek and A. Ouazzi and M. Nickaeen},
  title = {Least-squares finite element methods for the Navier-Stokes equations for generalized Newtonian fluids},
  journal = {Proceedings in Applied Mathematics and Mechanics},
  year = {2014},
  volume = {14},
  pages = {623--624}
}
Steeger K, Schwarz A, Schröder J, Starke G and Müller B (2014), "On a least-squares formulation for hyperelastic, transversely isotropic problems", Proceedings in Applied Mathematics and Mechanics. Vol. 14, pp. 247-248.

[BibTeX]
BibTeX: 
@article{SteSchSchStaMue:2014:oal,
  author = {K. Steeger and A. Schwarz and J. Schröder and G. Starke and B. Müller},
  title = {On a least-squares formulation for hyperelastic, transversely isotropic problems},
  journal = {Proceedings in Applied Mathematics and Mechanics},
  year = {2014},
  volume = {14},
  pages = {247--248}
}
Kiefer B, Niederhaus C, Balzani D, Bobisch CA, Gerharz E, Kruggel-Emden H, Schwarz A, Thielbörger P and Weiss GN (2013), "Anreizsysteme--Eine Möglichkeit zur Verbesserung der universitären Lehre", Journal für Hochschuldidaktik. , pp. 1-2.

[BibTeX]
BibTeX: 
@article{kiefer2013anreizsysteme,
  author = {Kiefer, Björn and Niederhaus, Constanze and Balzani, Daniel and Bobisch, Christian A and Gerharz, Eva and Kruggel-Emden, Harald and Schwarz, Alexander and Thielbörger, Pierre and Weiss, Gregor NF},
  title = {Anreizsysteme--Eine Möglichkeit zur Verbesserung der universitären Lehre},
  journal = {Journal für Hochschuldidaktik},
  year = {2013},
  pages = {1--2}
}
Schwarz A, Schröder J, Serdas S, Turek S, Ouazzi A and Nickaeen M (2013), "Performance aspects of a mixed s-v LSFEM for the incompressible Navier-Stokes equations with improved mass conservation", Proceedings in Applied Mathematics and Mechanics. Vol. 13, pp. 513-514.

[BibTeX]
BibTeX: 
@article{SchSchSerTurOuaNic:2013:pao,
  author = {A. Schwarz and J. Schröder and S. Serdas and S. Turek and A. Ouazzi and M. Nickaeen},
  title = {Performance aspects of a mixed s-v LSFEM for the incompressible Navier-Stokes equations with improved mass conservation},
  journal = {Proceedings in Applied Mathematics and Mechanics},
  year = {2013},
  volume = {13},
  pages = {513--514}
}
Serdas S, Schwarz A, Schröder J, Turek S, Ouazzi A and Nickaeen M (2013), "Influence of higher interpolation orders in mixed LSFEM for the incompressible Navier-Stokes equations", Proceedings in Applied Mathematics and Mechanics. Vol. 13, pp. 310-302.

[BibTeX]
BibTeX: 
@article{SerSchSchTurOuaNic:2013:ioh,
  author = {S. Serdas and A. Schwarz and J. Schröder and S. Turek and A. Ouazzi and M. Nickaeen},
  title = {Influence of higher interpolation orders in mixed LSFEM for the incompressible Navier-Stokes equations},
  journal = {Proceedings in Applied Mathematics and Mechanics},
  year = {2013},
  volume = {13},
  pages = {310--302}
}
Steeger K, Schwarz A, Schröder J, Starke G and Müller B (2013), "Comparison of geometrically nonlinear LSFEM formulations based on different hyperelastic models", Proceedings in Applied Mathematics and Mechanics. Vol. 13, pp. 97-98.

[BibTeX]
BibTeX: 
@article{SteSchSchStaMue:2013:shp,
  author = {K. Steeger and A. Schwarz and J. Schröder and G. Starke and B. Müller},
  title = {Comparison of geometrically nonlinear LSFEM formulations based on different hyperelastic models},
  journal = {Proceedings in Applied Mathematics and Mechanics},
  year = {2013},
  volume = {13},
  pages = {97--98}
}
Wriggers P, Schröder J and Schwarz A (2013), "A finite element method for contact using a third medium", Computational Mechanics. Vol. 52, pp. 837-847.

[BibTeX]
BibTeX: 
@article{WriSchSch:2013:afe,
  author = {P. Wriggers and J. Schröder and A. Schwarz},
  title = {A finite element method for contact using a third medium},
  journal = {Computational Mechanics},
  year = {2013},
  volume = {52},
  pages = {837--847}
}
Schwarz A and Schröder J (2012), "On a reduced mixed s-v least-squares finite element formulation for the incompressible Navier-Stokes equations", Proceedings in Applied Mathematics and Mechanics. Vol. 12, pp. 455-456.

[BibTeX]
BibTeX: 
@article{SchSch:2012:oar,
  author = {A. Schwarz and J. Schröder},
  title = {On a reduced mixed s-v least-squares finite element formulation for the incompressible Navier-Stokes equations},
  journal = {Proceedings in Applied Mathematics and Mechanics},
  year = {2012},
  volume = {12},
  pages = {455--456}
}
Schwarz A, Schröder J, Starke G and Steeger K (2012), "Least-squares mixed finite elements for hyperelastic material models", In Report of the Workshop 1207 at the ``Mathematisches Forschungsinstitut Oberwolfach'' entitled ``Advanced Computational Engineering'', organized by O. Allix, C. Carstensen, J. Schröder, P. Wriggers. , pp. 470-472.

[BibTeX]
BibTeX: 
@inproceedings{SchSchStaSte:2012:lmf,
  author = {A. Schwarz and J. Schröder and G. Starke and K. Steeger},
  title = {Least-squares mixed finite elements for hyperelastic material models},
  booktitle = {Report of the Workshop 1207 at the ``Mathematisches Forschungsinstitut Oberwolfach'' entitled ``Advanced Computational Engineering'', organized by O. Allix, C. Carstensen, J. Schröder, P. Wriggers},
  year = {2012},
  pages = {470--472}
}
Starke G, Müller B, Schwarz A and Schröder J (2012), "Stress-displacement least squares mixed finite element approximation for hyperelastic materials", In Report of the Workshop 1207 at the ``Mathematisches Forschungsinstitut Oberwolfach'' entitled ``Advanced Computational Engineering'', organized by O. Allix, C. Carstensen, J. Schröder, P. Wriggers. , pp. 467-469.

[BibTeX]
BibTeX: 
@inproceedings{StaMueSchSch:2012:sls,
  author = {G. Starke and B. Müller and A. Schwarz and J. Schröder},
  title = {Stress-displacement least squares mixed finite element approximation for hyperelastic materials},
  booktitle = {Report of the Workshop 1207 at the ``Mathematisches Forschungsinstitut Oberwolfach'' entitled ``Advanced Computational Engineering'', organized by O. Allix, C. Carstensen, J. Schröder, P. Wriggers},
  year = {2012},
  pages = {467--469}
}
Steeger K, Schwarz A, Schröder J, Starke G and Müller B (2012), "Solving hyperelastic problems using mixed LSFEM", Proceedings in Applied Mathematics and Mechanics. Vol. 12, pp. 215-216.

[BibTeX]
BibTeX: 
@article{SteSchSchStaMue:2012:shp,
  author = {K. Steeger and A. Schwarz and J. Schröder and G. Starke and B. Müller},
  title = {Solving hyperelastic problems using mixed LSFEM},
  journal = {Proceedings in Applied Mathematics and Mechanics},
  year = {2012},
  volume = {12},
  pages = {215--216}
}
Schwarz A and Schröder J (2011), "A mixed least-squares formulation of the Navier-Stokes equations for incompressible Newtonian fluid flow", Proceedings in Applied Mathematics and Mechanics. Vol. 11, pp. 589-590.

[BibTeX]
BibTeX: 
@article{SchSch:2011:aml,
  author = {A. Schwarz and J. Schröder},
  title = {A mixed least-squares formulation of the Navier-Stokes equations for incompressible Newtonian fluid flow},
  journal = {Proceedings in Applied Mathematics and Mechanics},
  year = {2011},
  volume = {11},
  pages = {589--590}
}
Starke G, Schwarz A and Schröder J (2011), "Analysis of a modified First-Order System Least Squares Method for linear Elasticity with improved Momentum Balance", SIAM Journal on Numerical Analysis. Vol. 49, pp. 1006-1022.

[BibTeX]
BibTeX: 
@article{StaSchSch:2011:aoa,
  author = {G. Starke and A. Schwarz and J. Schröder},
  title = {Analysis of a modified First-Order System Least Squares Method for linear Elasticity with improved Momentum Balance},
  journal = {SIAM Journal on Numerical Analysis},
  year = {2011},
  volume = {49},
  pages = {1006-1022}
}
Steeger K, Schwarz A and Schröder J (2011), "A weighted least-squares mixed finite element formulation for quasi-incompressible elastodynamics", Proceedings in Applied Mathematics and Mechanics. Vol. 11(1), pp. 287-288.

[BibTeX]
BibTeX: 
@article{SteSchSch:2011:awl,
  author = {K. Steeger and A. Schwarz and J. Schröder},
  title = {A weighted least-squares mixed finite element formulation for quasi-incompressible elastodynamics},
  journal = {Proceedings in Applied Mathematics and Mechanics},
  year = {2011},
  volume = {11},
  number = {1},
  pages = {287--288}
}
Schwarz A, Schröder J and Starke G (2010), "A modified least-squares mixed finite element with improved momentum balance", International Journal for Numerical Methods in Engineering. Vol. 81, pp. 286-306.

[BibTeX]
BibTeX: 
@article{SchSchSta:2010:aml,
  author = {A. Schwarz and J. Schröder and G. Starke},
  title = {A modified least-squares mixed finite element with improved momentum balance},
  journal = {International Journal for Numerical Methods in Engineering},
  year = {2010},
  volume = {81},
  pages = {286--306}
}
Steeger K, Schwarz A and Schröder J (2010), "A least-squares mixed finite element for quasi-incompressible elastodynamics", Proceedings in Applied Mathematics and Mechanics. Vol. 10(1), pp. 219-220.

[BibTeX]
BibTeX: 
@article{SteSchSch:2010:als,
  author = {K. Steeger and A. Schwarz and J. Schröder},
  title = {A least-squares mixed finite element for quasi-incompressible elastodynamics},
  journal = {Proceedings in Applied Mathematics and Mechanics},
  year = {2010},
  volume = {10},
  number = {1},
  pages = {219--220}
}
Schwarz A (2009), "Least-Squares Mixed Finite Elements for Solid Mechanics". Thesis at: University Duisburg-Essen.

[BibTeX]
BibTeX: 
@phdthesis{Sch:2009:lsm,
  author = {Schwarz, A.},
  title = {Least-Squares Mixed Finite Elements for Solid Mechanics},
  school = {University Duisburg-Essen},
  year = {2009}
}
Schwarz A and Schröder J (2009), "An asymmetric least-squares mixed finite element for elasto-plasticity at small strains", Proceedings in Applied Mathematics and Mechanics. Vol. 9, pp. 235-236.

[BibTeX]
BibTeX: 
@article{SchSch:2009:aal,
  author = {A. Schwarz and J. Schröder},
  title = {An asymmetric least-squares mixed finite element for elasto-plasticity at small strains},
  journal = {Proceedings in Applied Mathematics and Mechanics},
  year = {2009},
  volume = {9},
  pages = {235--236}
}
Schwarz A and Schröder J (2009), "A modified least-squares finite element formulation for small strain plasticity", In Proceedings of ICCSM 2009.

[BibTeX]
BibTeX: 
@inproceedings{SchSch:2009:aml,
  author = {A. Schwarz and J. Schröder},
  title = {A modified least-squares finite element formulation for small strain plasticity},
  booktitle = {Proceedings of ICCSM 2009},
  year = {2009}
}
Schwarz A, Schröder J and Starke G (2009), "Least-squares mixed finite elements for small strain elasto-viscoplasticity", International Journal for Numerical Methods in Engineering. Vol. 77, pp. 1351-1370.

[BibTeX]
BibTeX: 
@article{SchSchSta:2009:lsm,
  author = {A. Schwarz and J. Schröder and G. Starke},
  title = {Least-squares mixed finite elements for small strain elasto-viscoplasticity},
  journal = {International Journal for Numerical Methods in Engineering},
  year = {2009},
  volume = {77},
  pages = {1351--1370}
}
Schwarz A, Schröder J and Steeger K (2009), "A modified least-squares Finite Element Formulation for Small Strain Plasticity", In Proceedings of the International Congress of Croatian Society of Mechanics (ICCSM), 2009.

[BibTeX]
BibTeX: 
@conference{SchSchSte:2011:amls,
  author = {A. Schwarz and J. Schröder and K. Steeger},
  title = {A modified least-squares Finite Element Formulation for Small Strain Plasticity},
  booktitle = {Proceedings of the International Congress of Croatian Society of Mechanics (ICCSM), 2009},
  year = {2009}
}
Schwarz A, Kampen A and Schröder J (2008), "On the construction of Raviart--Thomas finite element spaces". Thesis at: Institut für Mechanik, Universität Duisburg-Essen. (39)

[BibTeX]
BibTeX: 
@techreport{SchKamSch:2008:otc,
  author = {A. Schwarz and A. Kampen and J. Schröder},
  title = {On the construction of Raviart--Thomas finite element spaces},
  school = {Institut für Mechanik, Universität Duisburg-Essen},
  year = {2008},
  number = {39}
}
Schwarz A and Schröder J (2008), "An asymmetric mixed finite element for incompressible elasticity based on a modified least-squares formulation", Proceedings in Applied Mathematics and Mechanics. Vol. 8, pp. 10341-10342.

[BibTeX]
BibTeX: 
@article{SchSch:2008:aam,
  author = {A. Schwarz and J. Schröder},
  title = {An asymmetric mixed finite element for incompressible elasticity based on a modified least-squares formulation},
  journal = {Proceedings in Applied Mathematics and Mechanics},
  year = {2008},
  volume = {8},
  pages = {10341--10342}
}
Ricken T, Schwarz A and Bluhm J (2007), "A triphasic model of transversely isotropic biological tissue with applications to stress and biologically induced growth", Computational Materials Science. Vol. 39(1), pp. 124-136.

[BibTeX]
BibTeX: 
@article{RicSchBlu:2007:atmotibtwatsabig,
  author = {Tim Ricken and Alexander Schwarz and Joachim Bluhm},
  title = {A triphasic model of transversely isotropic biological tissue with applications to stress and biologically induced growth},
  journal = {Computational Materials Science},
  year = {2007},
  volume = {39},
  number = {1},
  pages = {124--136}
}
Schwarz A and Schröder J (2007), "Least-squares mixed finite elements with applications to anisotropic elasticity and viscoplasticity", Proceedings in Applied Mathematics and Mechanics. Vol. 7, pp. 4040043-4040044.

[BibTeX]
BibTeX: 
@article{SchSch:2007:lmf,
  author = {A. Schwarz and J. Schröder},
  title = {Least-squares mixed finite elements with applications to anisotropic elasticity and viscoplasticity},
  journal = {Proceedings in Applied Mathematics and Mechanics},
  year = {2007},
  volume = {7},
  pages = {4040043-4040044}
}
Ricken T, Schwarz A and Bluhm J (2006), "A Triphasic Theory for Growth in Biological Tissue – Basics and Applications", Materialwissenschaft und Werkstofftechnik. Vol. 37(6), pp. 446-456.

[BibTeX]
BibTeX: 
@article{RicSchBlu:2006:attfgibtbaa,
  author = {T. Ricken and A. Schwarz and J. Bluhm},
  title = {A Triphasic Theory for Growth in Biological Tissue – Basics and Applications},
  journal = {Materialwissenschaft und Werkstofftechnik},
  year = {2006},
  volume = {37},
  number = {6},
  pages = {446--456}
}
Schwarz A and Schröder J (2006), "A least square mixed finite element for plane elasticity", Proceedings in Applied Mathematics and Mechanics. Vol. 6, pp. 265-266.

[BibTeX]
BibTeX: 
@article{SchSch:2006:als,
  author = {A. Schwarz and J. Schröder},
  title = {A least square mixed finite element for plane elasticity},
  journal = {Proceedings in Applied Mathematics and Mechanics},
  year = {2006},
  volume = {6},
  pages = {265--266}
}
Schwarz A (2004), "Investigations to Second Order Derivatives within Meshfree Approximations". Thesis at: Institut für Mechanik, Universität Duisburg-Essen. (Diplomarbeit)

[BibTeX]
BibTeX: 
@techreport{Sch:2004:its,
  author = {A. Schwarz},
  title = {Investigations to Second Order Derivatives within Meshfree Approximations},
  school = {Institut für Mechanik, Universität Duisburg-Essen},
  year = {2004},
  number = {Diplomarbeit}
}

Stand: 30.04.2019

Dr.-Ing. Alexander Schwarz

Tel. +49(0)201/183-2681
Fax +49(0)201/183-2680
Room V15 S06 D87
alexander.schwarz@uni-due.de
As 2020

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Contact

University Duisburg-Essen

Faculty of Engineering
Departement of Civil Engineering
Institute of Mechanics
Universitätsstraße 15
Room V15 S06 D87
45141 Essen