A multiscale discontinuous galerkin method

Authors:
Pavel Bochev;Thomas J. R. Hughes;Guglielmo Scovazzi
Affiliations:
Computational Mathematics and Algorithms Department, Sandia National Laboratories, Albuquerque, NM;Institute for Computational Engineering and Science, The University of Texas at Austin, Austin, TX;Computational Physics R&D Department, Sandia National Laboratories, Albuquerque, NM
Venue:
LSSC'05 Proceedings of the 5th international conference on Large-Scale Scientific Computing
Year:
2005

Citing 5
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Abstract

We propose a new class of Discontinuous Galerkin (DG) methods based on variational multiscale ideas. Our approach begins with an additive decomposition of the discontinuous finite element space into continuous (coarse) and discontinuous (fine) components. Variational multiscale analysis is used to define an interscale transfer operator that associates coarse and fine scale functions. Composition of this operator with a donor DG method yields a new formulation that combines the advantages of DG methods with the attractive and more efficient computational structure of a continuous Galerkin method. The new class of DG methods is illustrated for a scalar advection-diffusion problem.