A pressure robust staggered discontinuous Galerkin method for the Stokes equations

TL;DR

This paper introduces a pressure robust staggered discontinuous Galerkin method for the Stokes equations that achieves optimal convergence and superconvergence on polygonal meshes, validated by numerical experiments.

Contribution

It develops a novel pressure robust DG method using divergence preserving velocity reconstruction, enabling pressure independent error estimates and superconvergence.

Findings

Optimal convergence for velocity and pressure proved.

Superconvergence of velocity approximation demonstrated.

Numerical experiments confirm theoretical results.

Abstract

In this paper we propose a pressure robust staggered discontinuous Galerkin method for the Stokes equations on general polygonal meshes by using piecewise constant approximations. We modify the right hand side of the body force in the discrete formulation by exploiting divergence preserving velocity reconstruction operator, which is the crux for pressure independent velocity error estimates. The optimal convergence for velocity gradient, velocity and pressure are proved. In addition, we are able to prove the superconvergence of velocity approximation by the incorporation of divergence preserving velocity reconstruction operator in the dual problem, which is also an important contribution of this paper. Finally, several numerical experiments are carried out to confirm the theoretical findings.