Geodesic
Convergence for stabilisation of degenerately convex minimisation problems
S. Bartels1 orcid ; Carsten Carstensen2 ; P. Plechac3 ; Andreas Prohl4
1Christian-Albrechts-Universität zu Kiel, Germany
2Humboldt-Universität zu Berlin, Germany
3University of Warwick, Coventry, UK
4Universität Tübingen, Germany
Interfaces and free boundaries, Tome 6 (2004) no. 2, pp. 253-269

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DOI

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.
DOI : 10.4171/ifb/99
Classification : 35-XX, 65-XX, 76-XX, 92-XX
Mots-clés : degenerate variational problems, convexification, stabilisation, strong convergence, Euler-Lagrange equations, calculus of variations

S. Bartels  1   ; Carsten Carstensen  2   ; P. Plechac  3   ; Andreas Prohl  4

1 Christian-Albrechts-Universität zu Kiel, Germany
2 Humboldt-Universität zu Berlin, Germany
3 University of Warwick, Coventry, UK
4 Universität Tübingen, Germany 
S. Bartels; Carsten Carstensen; P. Plechac; Andreas Prohl. Convergence for stabilisation of degenerately convex minimisation problems. Interfaces and free boundaries, Tome 6 (2004) no. 2, pp. 253-269. doi: 10.4171/ifb/99
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     title = {Convergence for stabilisation of degenerately convex minimisation problems},
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     pages = {253--269},
     year = {2004},
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     doi = {10.4171/ifb/99},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/99/}
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