Staggered DG Method with Small Edges for Darcy Flows in Fractured Porous Media

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Original languageEnglish
Article number83
Journal / PublicationJournal of Scientific Computing
Volume90
Issue number3
Online published29 Jan 2022
Publication statusPublished - Mar 2022

Abstract

In this paper, we present and analyze a staggered discontinuous Galerkin method for Darcy flows in fractured porous media on fairly general meshes. A staggered discontinuous Galerkin method and a standard conforming finite element method with appropriate inclusion of interface conditions are exploited for the bulk region and the fracture, respectively. Our current analysis works on fairly general polygonal elements even in the presence of small edges. We prove the optimal convergence estimates in L2 error for all the variables by exploiting the Ritz projection. Importantly, our error estimates are shown to be fully robust with respect to the heterogeneity and anisotropy of the permeability coefficients. Several numerical experiments including meshes with small edges and anisotropic meshes are carried out to confirm the theoretical findings. Finally, our method is applied in the framework of unfitted mesh.

Research Area(s)

  • Anisotropic meshes, Darcy flow, Fractured porous media, General meshes, Small edges, Staggered DG methods, Trace inequality, Unfitted meshes