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

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  • Department of Mathematics, The Chinese University of Hong Kong, Hong Kong SAR, China

Received date: 2020-08-25

  Revised date: 2020-11-17

  Online published: 2022-03-01

Supported by

The research of Eric Chung is partially supported by the Hong Kong RGC General Research Fund (Project numbers 14304719 and 14302018) and CUHK Faculty of Science Direct Grant 2019-20.

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.

Cite this article

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 . DOI: 10.1007/s42967-020-00106-1

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