Locking free and gradient robust H(div)-conforming HDG methods for linear elasticity

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Date
2020
Volume
2680
Issue
Journal
Series Titel
WIAS Preprints
Book Title
Publisher
Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik
Abstract

Robust discretization methods for (nearly-incompressible) linear elasticity are free of volume-locking and gradient-robust. While volume-locking is a well-known problem that can be dealt with in many different discretization approaches, the concept of gradient-robustness for linear elasticity is new. We discuss both aspects and propose novel Hybrid Discontinuous Galerkin (HDG) methods for linear elasticity. The starting point for these methods is a divergence-conforming discretization. As a consequence of its well-behaved Stokes limit the method is gradient-robust and free of volume-locking. To improve computational efficiency, we additionally consider discretizations with relaxed divergence-conformity and a modification which re-enables gradient-robustness, yielding a robust and quasi-optimal discretization also in the sense of HDG superconvergence.

Description
Keywords
Linear elasticity, nearly incompressible, locking phenomenon, volume-locking, gradient-robustness, discontinuous Galerkin, H(div)-conforming HDG methods
Citation
Fu, G., Lehrenfeld, C., Linke, A., & Streckenbach, T. (2020). Locking free and gradient robust H(div)-conforming HDG methods for linear elasticity (Vol. 2680). Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik. https://doi.org//10.20347/WIAS.PREPRINT.2680
License
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