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Preconditioning of discontinuous Galerkin discretizations of second order elliptic problems
Veselin Dobrev
Email: dobrev@math.tamu.edu
Postal address: 801 Spring Loop, Apt. 303, College Station, TX 77840
We consider two-grid preconditioning schemes in which the coarse-level spaces are defined on the same geometrical mesh as the fine-level discontinuous space. We show that this technique gives rise to uniform preconditioners and present numerical evidence confirming the theoretical results. We also consider multilevel extensions of the two-grid methods and show that the resulting preconditioners are uniform and optimal.