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Norm Preconditioners for discontinuous Galerkin hp-Finite Element methods.

By Emmanuil H. Georgoulis and Daniel Loghin

Abstract

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
OAI identifier: oai:lra.le.ac.uk:2381/4270

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  1. (1976). A generalized conjugate gradient method for nonsymmetric systems of linear equations, in doi
  2. (2003). A multilevel discontinuous Galerkin method, doi
  3. (2006). A multilevel domain decomposition method for discontinuous Galerkin methods. in preparation,
  4. (2006). A note on the design of hp-version interior penalty discontinuous galerkin finite element methods for degenerate problems., doi
  5. (2006). Adaptive preconditioners for nonlinear systems of equations, doi
  6. (1982). An interior penalty finite element method with discontinuous elements, doi
  7. (2003). An overlapping domain decomposition preconditioner for a class of discontinuous Galerkin approximations of advection-diffusion problems, doi
  8. (2004). Analysis of block preconditioners for saddle-point problems, doi
  9. (2005). Convergence of multigrid algorithms for interior penalty methods, doi
  10. (2004). Discontinuous Galerkin methods for first-order hyperbolic problems, doi
  11. (2003). Discontinuous Galerkin methods on shape-regular and anisotropic meshes, doi
  12. (2002). Discontinuous hp-finite element methods for advection-diffusion-reaction problems, doi
  13. (1999). GMRES discontinuous Galerkin solution of the compressible Navier-Stokes equations, doi
  14. (2006). hp-version interior penalty discontinuous galerkin finite element methods on anisotropic meshes., doi
  15. (1999). Improved energy estimates for interior penalty, constrained and discontinuous Galerkin methods for elliptic problems.
  16. (2001). Interior penalty discontinuous approximations of elliptic problems, doi
  17. (1996). Interior penalty preconditioners for mixed finite element approximations of elliptic problems, doi
  18. (1982). Iterative methods for large sparse non-symmetric systems of linear equations, doi
  19. (1996). Iterative Methods for Sparse Linear Systems, doi
  20. (1990). On the theory of equivalent operators and application to the numerical solution of uniformly elliptic partial differential equations, doi
  21. (2005). Optimal error estimates for the hp–version interior penalty discontinuous Galerkin finite element method, doi
  22. (2002). Performance of discontinuous Galerkin methods for elliptic PDEs, doi
  23. (2003). Poincare´-Friedrichs inequalities for piecewise H1 functions, doi
  24. (2003). Preconditioning methods for local discontinuous Galerkin discretizations, doi
  25. (1973). Second order equations with nonnegative characteristic form, doi
  26. (2001). Stabilised hp-finite element approximation of partial differential equations with nonnegative characteristic form, doi
  27. (2005). Stopping criteria for iterations in finite element methods., doi
  28. (2001). Two-level additive Schwarz methods for a discontinuous Galerkin approximation of second order elliptic problems, doi
  29. (2005). Two-level non-overlapping Schwarz preconditioners for a discontinuous Galerkin approximation of the biharmonic equation, doi
  30. (2000). Using Krylov-subspace iterations in discontinuous Galerkin methods for nonlinear reaction-diffusion systems, doi

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