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arXiv · 2207.12557

Analysis of an embedded-hybridizable discontinuous Galerkin method for Biot's consolidation model

Aycil Cesmelioglu·Jeonghun J. Lee·Sander Rhebergen
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Abstract

We present an embedded-hybridizable discontinuous Galerkin finite element method for the total pressure formulation of the quasi-static poroelasticity model. Although the displacement and the Darcy velocity are approximated by discontinuous piece-wise polynomials, $H(\text{div})$-conformity of these unknowns is enforced by Lagrange multipliers. The semi-discrete problem is shown to be stable and the fully discrete problem is shown to be well-posed. Additionally, space-time a priori error estimates are derived, and confirmed by numerical examples, that show that the proposed discretization is free of volumetric locking.

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Aycil Cesmelioglu, Jeonghun J. Lee, Sander Rhebergen. 2022-07-25. Analysis of an embedded-hybridizable discontinuous Galerkin method for Biot's consolidation model. https://arxiv.org/abs/2207.12557

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