Journal
JOURNAL OF COMPUTATIONAL PHYSICS
Volume 229, Issue 10, Pages 3664-3674Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2010.01.020
Keywords
p-Multigrid; Geometric multigrid; Discontinuous Galerkin; Convection-diffusion equation
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An improved p-multigrid algorithm for discontinuous Galerkin (DG) discretizations of convection-diffusion problems is presented. The general p-multigrid algorithm for DG discretizations involves a restriction from the p = 1 to p = 0 discontinuous polynomial solution spaces This restriction is problematic and has limited the efficiency of the p-multigrid method For purely diffusive problems, Helenbrook and Atkins have demonstrated rapid convergence using a method that restricts from a discontinuous to continuous polynomial solution space at p = 1 It is shown that this method is not directly applicable to the convection-diffusion (CD) equation because it results in a central-difference discretization for the convective term To remedy this, Ideas from the streamwise upwind Petrov-Galerkin (SUPG) formulation are used to devise a transition from the discontinuous to continuous space at p = 1 that yields an upwind discretization The results show that the new method converges rapidly for all Peclet numbers. (C) 2010 Elsevier Inc All rights reserved.
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