A new staggered DG method for the Brinkman problem robust in the Darcy and Stokes limits

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Original languageEnglish
Article number112986
Journal / PublicationComputer Methods in Applied Mechanics and Engineering
Online published14 Mar 2020
Publication statusPublished - 1 Jun 2020
Externally publishedYes


In this paper we propose a novel staggered discontinuous Galerkin method for the Brinkman problem on general polygonal meshes. The proposed method is robust in the Stokes and Darcy limits, in addition, hanging nodes can be automatically incorporated in the construction of the method, which are desirable features in practical applications. There are three unknowns involved in our formulation, namely velocity gradient, velocity and pressure. Unlike the original staggered DG formulation proposed for the Stokes equations in Kim et al. (2013), we relax the tangential continuity of velocity and enforce different staggered continuity properties for the three unknowns, which is tailored to yield an optimal L2 error estimates for velocity gradient, velocity and pressure independent of the viscosity coefficient. Moreover, by choosing suitable projection, superconvergence can be proved for L2 error of velocity. Finally, several numerical results illustrating the good performances of the proposed method and confirming the theoretical findings are presented.

Research Area(s)

  • Brinkman problem, Darcy law, General meshes, Staggered DG method, Stokes equations, Superconvergence