JournalsifbVol. 6, No. 2pp. 253–269

Convergence for stabilisation of degenerately convex minimisation problems

  • S. Bartels

    Christian-Albrechts-Universität zu Kiel, Germany
  • Carsten Carstensen

    Humboldt-Universität zu Berlin, Germany
  • P. Plechac

    University of Warwick, Coventry, UK
  • Andreas Prohl

    Universität Tübingen, Germany
Convergence for stabilisation of degenerately convex minimisation problems cover
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Abstract

Degenerate variational problems often result from a relaxation technique in effective numerical simulation of nonconvex minimisation problems. The relaxed energy density is the convex envelope of the original one and so convex but not strictly convex. Hence strong convergence of straightforward finite element approximations cannot be expected but is relevant in many applications. This paper establishes a modified discretization by stabilisation and proves its convergence in strong norms.

Cite this article

S. Bartels, Carsten Carstensen, P. Plechac, Andreas Prohl, Convergence for stabilisation of degenerately convex minimisation problems. Interfaces Free Bound. 6 (2004), no. 2, pp. 253–269

DOI 10.4171/IFB/99