, Volume 119, Issue 1, pp 21-47
Date: 30 Apr 2011

Multigrid algorithms for symmetric discontinuous Galerkin methods on graded meshes

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Abstract

We study a class of symmetric discontinuous Galerkin methods on graded meshes. Optimal order error estimates are derived in both the energy norm and the L 2 norm, and we establish the uniform convergence of V-cycle, F-cycle and W-cycle multigrid algorithms for the resulting discrete problems. Numerical results that confirm the theoretical results are also presented.