Article

Numerische Mathematik

, Volume 119, Issue 1, pp 21-47

First online:

Multigrid algorithms for symmetric discontinuous Galerkin methods on graded meshes

  • S. C. BrennerAffiliated withDepartment of Mathematics, Louisiana State UniversityCenter for Computation and Technology, Louisiana State University Email author 
  • , J. CuiAffiliated withDepartment of Mathematics, Louisiana State UniversityInstitute for Mathematics and its Applications, University of Minnesota
  • , T. GudiAffiliated withCenter for Computation and Technology, Louisiana State UniversityDepartment of Mathematics, Indian Institute of Science
  • , L.-Y. SungAffiliated withDepartment of Mathematics, Louisiana State University

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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.

Mathematics Subject Classification (2000)

65N30 5N15 65N55