A Multilevel Method for Discontinuous Galerkin Approximation of Three-dimensional Elliptic Problems
We construct optimal order multilevel preconditioners for interiorpenalty discontinuous Galerkin (DG) finite element discretizations of 3D elliptic boundary-value problems. A specific assembling process is proposed which allows us to characterize the hierarchical splitting locally. This is also the key for a local analysis of the angle between the resulting subspaces. Applying the corresponding two-level basis transformation recursively, a sequence of algebraic problems is generated. These discrete problems can be associated with coarse versions of DG approximations (of the solution to the original variational problem) on a hierarchy of geometrically nested meshes. The presented numerical results demonstrate the potential of this approach.
KeywordsElliptic Problem Discontinuous Galerkin Discontinuous Galerkin Method Multilevel Method Order Elliptic Problem
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