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arXiv · 1704.04512

Devising superconvergent HDG methods with symmetric approximate stresses for linear elasticity by $M$-decompositions

Bernardo Cockburn·Guosheng Fu
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Abstract

We propose a new tool, which we call $M$-decompositions, for devising superconvergent hybridizable discontinuous Galerkin (HDG) methods and hybridized-mixed methods for linear elasticity with strongly symmetric approximate stresses on unstructured polygonal/polyhedral meshes. We show that for an HDG method, when its local approximation space admits an $M$-decomposition, optimal convergence of the approximate stress and superconvergence of an element-by-element postprocessing of the displacement field are obtained. The resulting methods are locking-free. Moreover, we explicitly construct approximation spaces that admit $M$-decompositions on general polygonal elements. We display numerical results on triangular meshes validating our theoretical findings.

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Bernardo Cockburn, Guosheng Fu. 2017-04-14. Devising superconvergent HDG methods with symmetric approximate stresses for linear elasticity by $M$-decompositions. https://arxiv.org/abs/1704.04512

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