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

Houston, Paul; Jensen, Max; Suli, Endre

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.

Citation

Houston, P., Jensen, M., & Suli, E. (2002). hp-Discontinuous Galerkin Finite Element Methods with Least-Squares Stabilization. Journal of Scientific Computing, 17(1-4), 3-25. https://doi.org/10.1023/a%3A1015180009979

• Journal Article Type: Article
• Publication Date: Dec 1, 2002
• Deposit Date: Jul 19, 2007
• Journal: Journal of Scientific Computing
• Print ISSN: 0885-7474
• Electronic ISSN: 1573-7691
• Publisher: Springer
• Peer Reviewed: Peer Reviewed
• Volume: 17
• Issue: 1-4
• Pages: 3-25
• DOI: https://doi.org/10.1023/a%3A1015180009979
• Keywords: hp-finite element methods, Discontinuous Galerkin methods, Least-squares finite element methods, First order systems PDEs.
• Public URL: https://durham-repository.worktribe.com/output/1578864
• Publisher URL: http://www.springerlink.com/content/4209xc225nbeyah5/