Stability and Convergence of Spectral Mixed Discontinuous Galerkin Methods for 3D Linear Elasticity on Anisotropic Geometric Meshes

Wihler, Thomas P.; Wirz, Marcel (2020). Stability and Convergence of Spectral Mixed Discontinuous Galerkin Methods for 3D Linear Elasticity on Anisotropic Geometric Meshes. Journal of scientific computing, 82(2) Springer 10.1007/s10915-020-01153-9

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We consider spectral mixed discontinuous Galerkin finite element discretizations of the Lamé system of linear elasticity in polyhedral domains in R³. In order to resolve possible corner, edge, and corner-edge singularities, anisotropic geometric edge meshes consisting of hexahedral elements are applied. We perform a computational study on the discrete inf-sup stability of these methods, and especially focus on the robustness with respect to the Poisson ratio close to the incompressible limit (i.e. the Stokes system). Furthermore, under certain realistic assumptions (for analytic data) on the regularity of the exact solution, we illustrate numerically that the proposed mixed DG schemes converge exponentially in a natural DG norm.

Item Type:

Journal Article (Original Article)

Division/Institute:

08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematics

UniBE Contributor:

Wihler, Thomas and Wirz, Marcel

Subjects:

500 Science > 510 Mathematics

ISSN:

0885-7474

Publisher:

Springer

Language:

English

Submitter:

Michel Arthur Bik

Date Deposited:

20 Apr 2020 10:56

Last Modified:

20 Apr 2020 10:56

Publisher DOI:

10.1007/s10915-020-01153-9

ArXiv ID:

1908.04647

BORIS DOI:

10.7892/boris.141835

URI:

https://boris.unibe.ch/id/eprint/141835

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