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A multilevel discontinuous Galerkin method. (English) Zbl 1044.65084
With extended references to the major papers on the subject, this work analyzes mathematically multigrid techniques for two discontinuous Galerkin methods: one for elliptic problems and a second one for singular perturbed advection-diffusion problems. In the former case, the analysis predicts convergence rates of the multigrid method independent of the mesh size. In both cases, theoretical results are supported by numerical experiments.

MSC:
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
65F10 Iterative numerical methods for linear systems
65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
65F35 Numerical computation of matrix norms, conditioning, scaling
35B25 Singular perturbations in context of PDEs
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
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