, Volume 119, Issue 1, pp 21-47

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.

The work of the S. C. Brenner was supported in part by the National Science Foundation under Grant No. DMS 07-38028 and Grant No. DMS-07-13835. The work of the J. Cui and L.-Y. Sung was supported in part by the National Science Foundation under Grant No. DMS-07-13835.