A simple preconditioner for a discontinuous Galerkin method for the Stokes problem

TL;DR

This paper introduces a straightforward preconditioner for a divergence-free discontinuous Galerkin method solving the Stokes problem, enhancing computational efficiency by leveraging the velocity field's H(div)-conformity.

Contribution

The paper develops a novel, simple preconditioner tailored for an H(div)-conforming DG discretization of the Stokes problem, improving solver performance.

Findings

Preconditioner significantly accelerates convergence.

Velocity field remains divergence-free across the domain.

Method demonstrates robustness and efficiency.

Abstract

In this paper we construct Discontinuous Galerkin approximations of the Stokes problem where the velocity field is H(div)-conforming. This implies that the velocity solution is divergence-free in the whole domain. This property can be exploited to design a simple and effective preconditioner for the final linear system.