The Pressure-Robust Weak Galerkin Finite Element Method for Stokes-Darcy Problem

Abstract

In this paper, we propose a pressure-robust weak Galerkin (WG) finite element scheme to solve the Stokes-Darcy problem. To construct the pressure-robust numerical scheme, we use the divergence-free velocity reconstruction operator to modify the test function on the right side of the numerical scheme. This numerical scheme is easy to implement because it only need to modify the right side. We prove the error between the velocity function and its numerical solution is independent of the pressure function and viscosity coefficient. Moreover, the errors of the velocity function reach the optimal convergence orders under the energy norm, as validated by both theoretical analysis and numerical results.