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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.

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Correspondence to S. C. Brenner.

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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.

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Brenner, S.C., Cui, J., Gudi, T. et al. Multigrid algorithms for symmetric discontinuous Galerkin methods on graded meshes. Numer. Math. 119, 21–47 (2011). https://doi.org/10.1007/s00211-011-0379-y

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  • DOI: https://doi.org/10.1007/s00211-011-0379-y

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