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Journal of Scientific Computing
Published in: Journal of Scientific Computing 3/2021

01-03-2021

Locking-Free and Gradient-Robust \({\varvec{H}}({{\,\mathrm{{\text {div}}}\,}})\)-Conforming HDG Methods for Linear Elasticity

Authors: Guosheng Fu, Christoph Lehrenfeld, Alexander Linke, Timo Streckenbach

Published in: Journal of Scientific Computing | Issue 3/2021

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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: it assures that dominant gradient fields in the momentum balance do not lead to spurious displacements. 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.
previous article Complexity of Proximal Augmented Lagrangian for Nonconvex Optimization with Nonlinear Equality Constraints
next article Extremal Rearrangement Problems Involving Poisson’s Equation with Robin Boundary Conditions

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Appendix
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Metadata
Title
Locking-Free and Gradient-Robust -Conforming HDG Methods for Linear Elasticity
Authors
Guosheng Fu
Christoph Lehrenfeld
Alexander Linke
Timo Streckenbach
Publication date
01-03-2021
Publisher
Springer US
Published in
Journal of Scientific Computing / Issue 3/2021
Print ISSN: 0885-7474
Electronic ISSN: 1573-7691
DOI
https://doi.org/10.1007/s10915-020-01396-6

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