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Numerical Algorithms for the Simulation of Finite Plasticity with Microstructures

  • Carsten Carstensen
  • Dietmar Gallistl
  • Boris Krämer
Part of the Lecture Notes in Applied and Computational Mechanics book series (LNACM, volume 78)

Abstract

This article reports on recent developments in the analysis of finite element methods for nonlinear PDEs with enforced microstructures. The first part studies the convergence of an adaptive finite element scheme for the two-well problem in elasticity. The analysis is based on the relaxation of the classical model energy by its quasiconvex envelope. The second part aims at the computation of guaranteed lower energy bounds for the two-well problem with nonconforming finite element methods that involve a stabilization for the discrete linear Green strain tensor. The third part of the paper investigates an adaptive discontinuous Galerkin method for a degenerate convex problem from topology optimization and establishes some equivalence to nonconforming finite element schemes.

Keywords

Topology Optimization Posteriori Error Discontinuous Galerkin Method Energy Error Posteriori Error Estimator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Carsten Carstensen
    • 1
  • Dietmar Gallistl
    • 2
  • Boris Krämer
    • 1
  1. 1.Institut für MathematikHumboldt-Universität zu BerlinBerlinGermany
  2. 2.Institut für Numerische SimulationUniversität BonnBonnGermany

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