Norm Preconditioners for Discontinuous Galerkin $hp$-Finite Element Methods

EH Georgoulis, Daniel Loghin

Research output: Contribution to journalArticle

5 Citations (Scopus)


We consider a norm-preconditioning approach for the solution of discontinuous Galerkin finite element discretizations of second order partial differential equations with a non-negative characteristic form. 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.
Original languageEnglish
Pages (from-to)2447-2465
Number of pages19
JournalSIAM Journal on Scientific Computing
Issue number5
Publication statusPublished - 1 Jan 2008


  • discontinuous Galerkin
  • hp-finite element methods
  • preconditioning
  • second order PDE


Dive into the research topics of 'Norm Preconditioners for Discontinuous Galerkin $hp$-Finite Element Methods'. Together they form a unique fingerprint.

Cite this