A Multiscale Discontinuous Galerkin Method

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. Then, 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 key to the success of the new approach is efficient computation of the interscale operator. Variational Multiscale Analysis leads to a natural definition of local, elementwise problems that mimic the structure of the donor DG formulation. The new class of DG methods is illustrated for a model scalar advection-diffusion boundary value problem.

• Type: Conference
• Year: 2005
• Where: LSSC
• Authors: Pavel B. Bochev, Thomas J. R. Hughes, Guglielmo Scovazzi
• Keywords: Dg Methods, Donor Dg, LSSC 2005, Variational Multiscale Analysis