On the Coupling of Local Discontinuous Galerkin and Conforming Finite Element Methods

Authors:
Ilaria Perugia;Dominik Schötzau
Affiliations:
Department of Mathematics, University of Pavia, Via Ferrata 1, 27100 Pavia, Italy. perugia@dimat.unipv.it;School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455. schoetza@math.umn.edu
Venue:
Journal of Scientific Computing
Year:
2002

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Abstract

The finite element formulation resulting from coupling the local discontinuous Galerkin method with a standard conforming finite element method for elliptic problems is analyzed. The transmission conditions across the interface separating the subdomains where the different formulations are applied are taken into account by a suitable definition of the so-called numerical fluxes. An error analysis leading to optimal a priori error estimates is presented for arbitrary meshes with possible hanging nodes. Numerical experiments validating the theoretical results are reported.