hp-Discontinuous Galerkin Finite Element Methods with Least-Squares Stabilization

Authors:
Paul Houston;Max Jensen;Endre Süli
Affiliations:
Department of Mathematics & Computer Science, University of Leicester, Leicester LE1 7RH, United Kingdom. Paul.Houston@mcs.le.ac.uk;Oxford University Computing Laboratory, Wolfson Building, Parks Road, Oxford OX1 3QD, United Kingdom. Max.Jensen@comlab.ox.ac.uk;Oxford University Computing Laboratory, Wolfson Building, Parks Road, Oxford OX1 3QD, United Kingdom. endre@comlab.ox.ac.uk
Venue:
Journal of Scientific Computing
Year:
2002

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Abstract

We consider a family of hp-version discontinuous Galerkin finite element methods with least-squares stabilization for symmetric systems of first-order partial differential equations. The family includes the classical discontinuous Galerkin finite element method, with and without streamline-diffusion stabilization, as well as the discontinuous version of the Galerkin least-squares finite element method. An hp-optimal error bound is derived in the associated DG-norm. If the solution of the problem is elementwise analytic, an exponential rate of convergence under p-refinement is proved. We perform numerical experiments both to illustrate the theoretical results and to compare the various methods within the family.