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

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.

arXiv comment30 pages

References in corpus (9)

• A finite element method with strong mass conservation for Biot's linear consolidation model
• A hybridizable discontinuous Galerkin method for the Navier--Stokes equations with pointwise divergence-free velocity field
• Partitioning strategies for the interaction of a fluid with a poroelastic material based on a Nitsche's coupling approach
• Analysis of the coupled Navier-Stokes/Biot problem
• Robust error analysis of coupled mixed methods for Biot's consolidation model
• Analysis of a hybridized/interface stabilized finite element method for the Stokes equations
• An embedded--hybridized discontinuous Galerkin finite element method for the Stokes equations
• The Biot-Stokes coupling using total pressure: formulation, analysis and application to interfacial flow in the eye
• An embedded-hybridized discontinuous Galerkin method for the coupled Stokes-Darcy system