Publication details for Dr Max JensenHouston, Paul, Jensen, Max & Suli, Endre (2002). hp-Discontinuous Galerkin Finite Element Methods with Least-Squares Stabilization. Journal of Scientific Computing 17(1-4): 3-25.
- Publication type: Journal papers: academic
- ISSN/ISBN: 0885-7474, 1573-7691
- DOI: 10.1023/A:1015180009979
- Keywords: hp-finite element methods, discontinuous Galerkin methods, least-squares finite element methods, first order systems of PDEs
- View online: Online version
- Durham research online: DRO record
Author(s) from Durham
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.