# On the Strong Convergence of Gradients in Stabilized Degenerate Convex Minimization Problems

@article{Boiger2010OnTS, title={On the Strong Convergence of Gradients in Stabilized Degenerate Convex Minimization Problems}, author={Wolfgang Boiger and Carsten Carstensen}, journal={SIAM J. Numer. Anal.}, year={2010}, volume={47}, pages={4569-4580} }

Infimizing sequences in nonconvex variational problems typically exhibit enforced finer and finer oscillations called microstructures such that the infimal energy is not attained. Although those oscillations are physically meaningful, finite element approximations experience difficulty in their reconstruction. The relaxation of the nonconvex minimization problem by (semi) convexification leads to a macroscopic model for the effective energy. The resulting discrete macroscopic problem is…

## 7 Citations

### Stabilised finite element approximation for degenerate convex minimisation problems

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- 2013

Infimising sequences of nonconvex variational problems often do not converge strongly in Sobolev spaces due to fine oscillations. These oscillations are physically meaningful; finite element…

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Strong convergence of the stress even without any smoothness assumption for a class of stabilised degenerate convex minimisation problems and an improved a posteriori error control is presented, which narrows the efficiency reliability gap.

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- Computer ScienceJ. Sci. Comput.
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It will be proven that this stabilization technique leads to a posteriori error control on unstructured triangulations, and so enables the use of adaptive algorithms.

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- 2015

An adaptive discontinuous Galerkin method for a degenerate convex problem from topology optimization is investigated and some equivalence to nonconforming finite element schemes is established.

### Rate-Independent versus Viscous Evolution of Laminate Microstructures in Finite Crystal Plasticity

- Engineering
- 2015

In this chapter we investigate the variational modeling of the evolution of inelastic microstructures by the example of finite crystal plasticity with one active slip system. For this purpose we…

### Stabilized FEM for Some Optimal Design Problem

- Materials ScienceJournal of Scientific Computing
- 2017

Some optimal design problems in topology optimization eventually lead to degenerate convex minimization problems E(v):=∫ΩW(∇v)dx-∫Ωfvdx\documentclass[12pt]{minimal} \usepackage{amsmath}…

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