Weak Galerkin method for the coupled Darcy-Stokes flow

TL;DR

This paper introduces a weak Galerkin finite element method for solving coupled Darcy-Stokes flow equations, effectively handling interface conditions and enabling strong coupling in the discrete space.

Contribution

The paper develops a novel weak Galerkin discretization for Darcy-Stokes flow that explicitly enforces normal velocity continuity and provides error estimates.

Findings

Achieves strong coupling in the discrete space.

Provides error estimates for various finite element choices.

Handles interface conditions effectively.

Abstract

A family of weak Galerkin finite element discretization is developed for solving the coupled Darcy-Stokes equation. The equation in consideration admits the Beaver-Joseph-Saffman condition on the interface. By using the weak Galerkin approach, in the discrete space we are able to impose the normal continuity of velocity explicitly. Or in other words, strong coupling is achieved in the discrete space. Different choices of weak Galerkin finite element spaces are discussed, and error estimates are given.