The pressure-robust weak Galerkin finite element method for Stokes-Darcy problem

TL;DR

This paper introduces a pressure-robust weak Galerkin finite element method for the Stokes-Darcy problem, ensuring velocity accuracy independent of pressure and viscosity, with proven optimal convergence.

Contribution

It develops a novel pressure-robust scheme using divergence-free velocity reconstruction, improving accuracy and robustness over existing methods.

Findings

Velocity error independent of pressure and viscosity

Achieves optimal convergence orders for velocity and pressure

Validated by theoretical analysis and numerical experiments

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. 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 and the pressure function reach the optimal convergence orders under the energy norm, as validated by both theoretical analysis and numerical results.