Convergence of a stabilized discontinuous Galerkin method for incompressible nonlinear elasticity

Davide Baroli, Alfio Quarteroni, Ricardo Ruiz-Baier

Research output: Contribution to journalArticleResearchpeer-review

10 Citations (Scopus)

Abstract

In this paper we present a discontinuous Galerkin method applied to incompressible nonlinear elastostatics in a total Lagrangian deformation-pressure formulation, for which a suitable interior penalty stabilization is applied. We prove that the proposed discrete formulation for the linearized problem is well-posed, asymptotically consistent and that it converges to the corresponding weak solution. The derived convergence rates are optimal and further confirmed by a set of numerical examples in two and three spatial dimensions.

Original languageEnglish
Pages (from-to)425-443
Number of pages19
JournalAdvances in Computational Mathematics
Volume39
Issue number2
DOIs
Publication statusPublished - 1 Aug 2013
Externally publishedYes

Keywords

  • Discontinuous Galerkin formulation
  • Edge-based stabilization
  • Incompressible material
  • Nonlinear elasticity

Cite this