A mixed finite element method for nonlinear elasticity: Two-fold saddle point approach and a-posteriori error estimate

Mauricio A. Barrientos, Gabriel N. Gatics, Ernst P. Stephan

Research output: Contribution to journalArticlepeer-review

37 Scopus citations

Abstract

We extend the applicability of stable mixed finite elements for linear plane elasticity, such as PEERS, to a mixed variational formulation of hyperelasticity. The present approach is based on the introduction of the strain tensor as a further unknown, which yields a two-fold saddle point nonlinear operator equation for the corresponding weak formulation. We provide the uniqueness of solution for the continuous and discrete schemes, and derive the usual Cea estimate for the associated error. Finally, a reliable a-posteriori error estimate, based on the solution of local Dirichlet problems, and well suited for adaptive computations, is also given.

Original languageEnglish
Pages (from-to)197-222
Number of pages26
JournalNumerische Mathematik
Volume91
Issue number2
DOIs
StatePublished - Apr 2002
Externally publishedYes

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