97-2   Berichtsreihe des Mathematischen Seminars der Universität Kiel

Carsten Carstensen, Petr Plechac:

Adaptive mesh refinement in scalar non-convex variational problems

Since direct numerical solution of a non-convex variational problem \MINP\ yields rapid oscillations, we study the relaxed problem \MINRP\ which is a degenerate convex minimisation problem. The classical example for such a relaxed variational problem is the double-well problem. In an earlier work, the authors showed that relaxation is not linked to a loss of information if our main interest concerns the macroscopic displacement field, the stress field or the microstructure. Furthermore, a~priori and a~posteriori error estimates have been computed and an adaptive algorithm was proposed for this class of degenerate variational problems. This paper addresses the question of efficiency and considers the ZZ-indicator, named after Zienkiewic and Zhu, and discusses its performance compared with the rigorous indicator introduced by the authors.


Mail an Jens Burmeister
[Thu Feb 19 18:56:33 2009]
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