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arXiv · 2207.12568

Hybridizable discontinuous Galerkin methods for the coupled Stokes--Biot problem

Aycil Cesmelioglu·Jeonghun J. Lee·Sander Rhebergen
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Abstract

We present and analyze a hybridizable discontinuous Galerkin (HDG) finite element method for the coupled Stokes--Biot problem. Of particular interest is that the discrete velocities and displacement are $H(\text{div})$-conforming and satisfy the compressibility equations pointwise on the elements. Furthermore, in the incompressible limit, the discretization is strongly conservative. We prove well-posedness of the discretization and, after combining the HDG method with backward Euler time stepping, present a priori error estimates that demonstrate that the method is free of volumetric locking. Numerical examples further demonstrate optimal rates of convergence in the $L^2$-norm for all unknowns and that the discretization is locking-free.

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Aycil Cesmelioglu, Jeonghun J. Lee, Sander Rhebergen. 2022-07-25. Hybridizable discontinuous Galerkin methods for the coupled Stokes--Biot problem. https://doi.org/10.1016/j.camwa.2023.05.024

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