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