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Robust smoothers for high-order discontinuous Galerkin discretizations of advection–diffusion problems

Authors
Journal
Journal of Computational and Applied Mathematics
0377-0427
Publisher
Elsevier
Publication Date
Volume
218
Issue
1
Identifiers
DOI: 10.1016/j.cam.2007.04.032
Keywords
  • Multigrid
  • Discontinuous Galerkin
  • Finite Elements
  • Advection
  • High Order

Abstract

Abstract The multigrid method for discontinuous Galerkin (DG) discretizations of advection–diffusion problems is presented. It is based on a block Gauss–Seidel smoother with downwind ordering honoring the advection operator. The cell matrices of the DG scheme are inverted in this smoother in order to obtain robustness for higher order elements. Employing a set of experiments, we show that this technique actually yields an efficient preconditioner and that both ingredients, downwind ordering and blocking of cell matrices are crucial for robustness.

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