Advancements in the Computational Calculus of Variations
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The aim of this paper is a survey on some state-of-the-art techniques in the numerical analysis of minimisation problems in nonlinear elasticity and on the concepts of quasi and polyconvexity in the calculus of variations. The issue of the approximation of singular minimisers is addressed via a penalty finite element method (PFEM) and macroscopic deformations are computed via the relaxation finite element method (RFEM). New numerical results are presented for the scalar doublewell problem as a benchmark in computational microstructures with adaptive meshrefining, in order to recover optimal convergence in the presence of singularities at interfaces.
KeywordsPosteriori Error Nonlinear Elasticity Posteriori Error Estimate Young Measure Relax Problem
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