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

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Original languageEnglish
Pages (from-to)205–226
Journal / PublicationCommunications on Applied Mathematics and Computation
Issue number1
Online published15 Jul 2021
Publication statusPublished - Mar 2022
Externally publishedYes


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.

Research Area(s)

  • Staggered DG method, Brinkman-Forchheimer, General meshes, Uniformly stable