Adaptive Approximation of Young Measure Solutions in Scalar Nonconvex Variational Problems

Keywords

Mathematics, A priori and a posteriori, Scalar (mathematics), Measure (data warehouse), Applied mathematics

References

• Parametrized measures and variational principlesPablo Pedregal — 1997
• Optimization And Nonsmooth AnalysisFrank H. Clarke — 1983
• Relaxation in Optimization Theory and Variational CalculusTomáš Roubı́ček — 1997
• Local Stress Regularity in Scalar Nonconvex Variational ProblemsCarsten Carstensen, Stefan Müller — 2002
• Constitutive theory for some constrained elastic crystalsJ. L. Ericksen — 1986
• Numerical approximation of parametrized measuresPablo Pedregal — 1995
• Computation of Microstructure Utilizing Young Measure RepresentationsR. A. Nicolaides, Noel J. Walkington — 1993
• Weak convergence of integrands and the young measure representationDavid Kinderlehrer, Pablo Pedregal — 1992
• Numerical Approach to Double Well ProblemsMartin Kružík — 1998
• HOPDM (version 2.12) — A fast LP solver based on a primal-dual interior point methodJacek Gondzio — 1995
• QUASI-INTERPOLATION AND A POSTERIORI ERROR ANALYSIS IN FINITE ELEMENT METHODSCarsten Carstensen — 1999
• Inhomogeneous Dirichlet conditions in a priori and a posteriori finite element error analysisSören Bartels, Carsten Carstensen, Georg Dolzmann — 2004
• Numerical solution of the scalar double-well problem allowing microstructureCarsten Carstensen, Petr Plecháč — 1997
• Optimal order error estimates for the finite element approximation of the solution of a nonconvex variational problemCharles Collins, Mitchell Luskin — 1991
• Young measure approximation in micromagneticsMartin Kružík, Andreas Prohl — 2001
• On the computation of crystalline microstructureMitchell Luskin — 1996
• Each averaging technique yields reliable a posteriori error control in FEM on unstructured grids. Part I: Low order conforming, nonconforming, and mixed FEMCarsten Carstensen, Sören Bartels — 2002
• On the dynamics of fine structureJ. M. Ball, Philip Holmes, Richard D. James — 1991
• The finite element method for elliptic problemsPhilippe G. Ciarlet — 2002
• Each averaging technique yields reliable a posteriori error control in FEM on unstructured grids. Part II: Higher order FEMSören Bartels, Carsten Carstensen — 2002

Cited by

• DISCRETIZATION METHODS FOR SEMILINEAR PARABOLIC OPTIMAL CONTROL PROBLEMSI. Chryssoverghi — 2006
• FE-BE coupling for a transmission problem involving microstructureHeiko Gimperlein, Matthias Maischak, Elmar Schrohe — 2010
• Using discrete optimization algorithms to find minimum energy configurations of slender cantilever beams with non-convex energy functionsKrishna R. Narayanan, Arun R. Srinivasa — 2009
• Linear convergence in the approximation of rank-one convex envelopesSören Bartels — 2004
• Linear-programming approach to nonconvex variational problemsSören Bartels, Tomáš Roubı́ček — 2004
• Coarse-Convex-Compactification Approach to Numerical Solution of Nonconvex Variational ProblemsRené Meziat, Tomáš Roubı́ček, Diego Patiño — 2010
• Computational Microstructures in Phase Transition Solids and Finite‐Strain ElastoplasticityCarsten Carstensen, Klaus Hackl, H. Ulrich Hoppe — 2006
• Discretization-Optimization Methods for Nonlinear Parabolic Relaxed Optimal Control Problems with State ConstraintsI. Chryssoverghi, Jürgen Geiser, Al-Hawasy, J. — 2006
• FE-BE coupling for a transmission problem involving microstructureHeiko Gimperlein, Matthias Maischak, Ernst P. Stephan — 2021
• Nonconvex energy minimisation and relaxation in computational material scienceC. Carstensen — 2003
• Relaxation and the Computation of Effective Energies and Microstructures in Solid MechanicsC. Carstensen, S. Bartels, K. Hackl — 2006
• Numerical Techniques in Relaxed Optimization ProblemsT. Roubíček — 2006
• Descent-Penalty Methods for Relaxed Nonlinear Elliptic Optimal Control ProblemsI. Chryssoverghi, J. Geiser — 2009
• Discretization-Optimization Methods for Nonlinear Elliptic Relaxed Optimal Control Problems with State ConstraintsI. Chryssoverghi, J. Coletsos, J. Geiser — 2005
• Classical and Relaxed Optimization Methods for Nonlinear Parabolic Optimal Control ProblemsI. Chryssoverghi, J. Coletsos, B. Kokkinis — 2009

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