An embedded-hybridized discontinuous Galerkin method for the coupled Stokes-Darcy system

Abstract

We introduce an embedded-hybridized discontinuous Galerkin (EDG-HDG) method for the coupled Stokes-Darcy system. This EDG-HDG method is a pointwise mass-conserving discretization resulting in a divergence-conforming velocity field on the whole domain. In the proposed scheme, coupling between the Stokes and Darcy domains is achieved naturally through the EDG-HDG facet variables. \emph{A priori} error analysis shows optimal convergence rates, and that the velocity error does not depend on the pressure. The error analysis is verified through numerical examples on unstructured grids for different orders of polynomial approximation.

References in corpus (1)

• An embedded--hybridized discontinuous Galerkin finite element method for the Stokes equations

Cited by in corpus (7)

• HDGlab: An open-source implementation of the hybridisable discontinuous Galerkin method in MATLAB
• An exactly mass conserving space-time embedded-hybridized discontinuous Galerkin method for the Navier-Stokes equations on moving domains
• Hybridizable discontinuous Galerkin methods for the coupled Stokes--Biot problem
• A hybridizable discontinuous Galerkin method for the coupled Navier-Stokes and Darcy problem
• A hybridizable discontinuous Galerkin method for the fully coupled time-dependent Stokes/Darcy-transport problem
• A conforming sliding mesh technique for an embedded-hybridized discontinuous Galerkin discretization for fluid-rigid body interaction
• A compatible embedded-hybridized discontinuous Galerkin method for the Stokes--Darcy-transport problem