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Norm Preconditioners for discontinuous Galerkin hp-Finite Element methods.

By Emmanuil H. Georgoulis and Daniel Loghin


We consider a norm-preconditioning approach for the solution of discontinuous Galerkin finite element discretizations of second order PDE with non-negative characteristic form. In particular, we perform an analysis for the general case of discontinuous hp-finite element discretizations. Our solution method is a norm-preconditioned three-term GMRES routine. We find that for symmetric positive-definite diffusivity tensors the convergence of our solver is independent of discretization, while for the semidefinite case both theory and experiment indicate dependence on both h and p. Numerical results are included to illustrate performance on several test cases

Publisher: Dept. of Mathematics, University of Leicester.
Year: 2006
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