Adaptive algorithms for scalar non-convex variational problems

Carsten Carstensen, Petr Plecháč

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)


Since direct numerical solution of a non-convex variational problem (P) yields rapid oscillations, we study the relaxed problem (RP) which is a degenerate convex minimization 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 Zienkiewicz and Zhu, and discusses its performance compared with the rigorous indicator introduced by the authors. © 1998 Elsevier Science B. V.

Original languageEnglish
Pages (from-to)203-216
Number of pages14
JournalApplied Numerical Mathematics
Issue number1-2
Publication statusPublished - Jan 1998


  • A posteriori error estimates
  • Adaptive algorithms
  • Microstructure
  • Non-convex minimization
  • Young measures
  • Zz-estimator


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