A Uniformly Robust Staggered DG Method for the Unsteady Darcy-Forchheimer-Brinkman Problem

doi:10.1007/s42967-020-00106-1

Abstract

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 fexibly 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 confrm the theoretical fndings.

Key words: Staggered DG method, Brinkman-Forchheimer, General meshes, Uniformly stable

CLC Number:

Lina Zhao, Ming Fai Lam, Eric Chung. A Uniformly Robust Staggered DG Method for the Unsteady Darcy-Forchheimer-Brinkman Problem[J]. Communications on Applied Mathematics and Computation, 2022, 4(1): 205-226.

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