Hybridizable discontinuous Galerkin methods for the coupled Stokes–Biot problem

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(div)-conforming and satisfy the compressibility equations pointwise on the elements. Furthermore...

Full description

Saved in:
Bibliographic Details
Published in:Computers & mathematics with applications (1987) 2023-08, Vol.144, p.12-33
Main Authors: Cesmelioglu, Aycil, Lee, Jeonghun J., Rhebergen, Sander
Format: Article
Language:English
Subjects:
Beavers–Joseph–Saffman
Biot's consolidation model
Discontinuous Galerkin
Hybridized methods
Poroelasticity
Stokes equations
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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(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 L2-norm for all unknowns and that the discretization is locking-free.
ISSN:0898-1221
1873-7668
DOI:10.1016/j.camwa.2023.05.024