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

Journal Article · Tue Mar 17 00:00:00 EDT 2020 · Journal of Scientific Computing

DOI:https://doi.org/10.1007/s10915-020-01191-3· OSTI ID:1802634

Wang, Fei ^[1]; Wu, Shuonan ^[2]; Xu, Jinchao ^[3]

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1. Xi'an Jiaotong Univ. (China). State Key Lab. of Multiphase Flow in Power Engineering; OSTI
2. Peking Univ., Beijing (China)
3. Pennsylvania State Univ., University Park, PA (United States)

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 (\(k\ge 0\)). The mixed DG scheme is proved to be well-posed under proper norms. Specifically, we prove that, for any \(k \ge 0\), the \(H(\mathrm{div})\)-like error estimate for the stress and \(L^2\) error estimate for the displacement are optimal. We further establish the optimal \(L^2\) error estimate for the stress provided that the \({\mathcal {P}}_{k+2}-{\mathcal {P}}_{k+1}^{-1}\) Stokes pair is stable and \(k \ge d\). Finally, we also provide numerical results of MDG showing that the orders of convergence are actually sharp.

• Research Organization: Pennsylvania State Univ., University Park, PA (United States)
• Sponsoring Organization: USDOE Office of Science (SC)
• Grant/Contract Number: SC0014400
• OSTI ID: 1802634
• Journal Information: Journal of Scientific Computing, Journal Name: Journal of Scientific Computing Journal Issue: 1 Vol. 83; ISSN 0885-7474
• Publisher: Springer
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING
A priori error analysis
Linear elasticity
Mixed DG method
Well-posedness