A uniformly robust staggered DG method for the unsteady Darcy-Forchheimer-Brinkman problem

TL;DR

This paper introduces a robust staggered discontinuous Galerkin method for the unsteady Darcy-Forchheimer-Brinkman problem, achieving uniform accuracy across various mesh types and pressure conditions.

Contribution

It presents a novel staggered DG scheme that relaxes tangential velocity continuity, ensuring uniform robustness and pressure-independent velocity error estimates.

Findings

The method is well-posed and stable.

Error estimates are independent of pressure.

Numerical experiments confirm theoretical results.

Abstract

In this paper we propose and analyze a uniformly robust staggered DG method for the unsteady Darcy-Forchheimer-Brinkman problem. Our formulation is based on velocity gradient-velocity-pressure and the resulting scheme can be flexibly applied to fairly general polygonal meshes. We relax the tangential continuity for velocity, which is the key ingredient in achieving the uniform robustness. We present well-posedness and error analysis for both the semi-discrete scheme and the fully discrete scheme, and the theories indicate that the error estimates for velocity are independent of pressure. Several numerical experiments are presented to confirm the theoretical findings.