A Mixed Discontinuous Galerkin Method for Linear Elasticity with Strongly Imposed Symmetry

Fei Wang, Shuonan Wu, Jinchao Xu

Research output: Contribution to journalArticle

1 Scopus citations

Abstract

In this paper, we study a mixed discontinuous Galerkin (MDG) method to solve linear elasticity problem with arbitrary order discontinuous finite element spaces in d-dimension (d= 2 , 3). This method uses polynomials of degree k+ 1 for the stress and of degree k for the displacement (k≥ 0). The mixed DG scheme is proved to be well-posed under proper norms. Specifically, we prove that, for any k≥ 0 , the H(div) -like error estimate for the stress and L2 error estimate for the displacement are optimal. We further establish the optimal L2 error estimate for the stress provided that the Pk+2-Pk+1-1 Stokes pair is stable and k≥ d. We also provide numerical results of MDG showing that the orders of convergence are actually sharp.

Original languageEnglish (US)
Article number2
JournalJournal of Scientific Computing
Volume83
Issue number1
DOIs
StatePublished - Apr 1 2020

All Science Journal Classification (ASJC) codes

  • Software
  • Theoretical Computer Science
  • Numerical Analysis
  • Engineering(all)
  • Computational Theory and Mathematics
  • Computational Mathematics
  • Applied Mathematics

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