Coupling discontinuous galerkin and mixed finite element discretizations using mortar finite elements

Vivette Girault*, Shuyu Sun, Mary F. Wheeler, Ivan Yotov

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

42 Scopus citations

Abstract

Discontinuous Galerkin (DG) and mixed finite element (MFE) methods are two popular methods that possess local mass conservation. In this paper we investigate DG-DG and DG-MFE domain decomposition couplings using mortar finite elements to impose weak continuity of fluxes and pressures on the interface. The subdomain grids need not match, and the mortar grid may be much coarser, giving a two-scale method. Convergence results in terms of the fine subdomain scale h and the coarse mortar scale H are established for both types of couplings. In addition, a nonoverlapping parallel domain decomposition algorithm is developed, which reduces the coupled system to an interface mortar problem. The properties of the interface operator are analyzed.

Original languageEnglish (US)
Pages (from-to)949-979
Number of pages31
JournalSIAM Journal on Numerical Analysis
Volume46
Issue number2
DOIs
StatePublished - Nov 12 2008

Keywords

  • Discontinuous Galerkin
  • Flow in porous media
  • Interface problem
  • Mixed finite element
  • Mortar finite element

ASJC Scopus subject areas

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

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