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

2019/02/23 by Fei Wang, Shuonan Wu, Wang, Fei +3 · 1 citation
Engineering · Computer Science · #Advanced Numerical Methods in Computational Mathematics #Advanced Mathematical Modeling in Engineering #Numerical methods in engineering

paper · pdf · doi:10.48550/arxiv.1902.08717

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(\rm 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 P_k+2-P_k+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.

Citations

• Mixed finite elements for elasticity
• Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems

Cited by

• A Least Squares Weak Galerkin Framework for Linear Elasticity on Polytopal Meshes

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