Norm Preconditioners for Discontinuous Galerkin hp-Finite Element Methods

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 threeterm 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.

• Type: Journal
• Year: 2008
• Where: SIAMSC
• Authors: Emmanuil H. Georgoulis, Daniel Loghin
• Keywords: Discontinuous Hp-finite Element, Element Discretizations, Non-negative Characteristic Form, SIAMSC 2008