Stabilizedhp-Finite Element Methods for First-Order Hyperbolic Problems
Authors:
- Paul HoustonPHPaul Houston
- Christoph SchwabCSChristoph Schwab
- Endre SüliESEndre Süli
- 1 January 2000
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Numerical Analysis
- Vol. 37 (5) , 1618-1643
Abstract
We analyze the hp-version of the streamline-diffusion finite element method (SDFEM) and of the discontinuous Galerkin finite element method (DGFEM) for first-order linear hyperbolic problems. For both methods, we derive new error estimates on general finite element meshes which are sharp in the mesh-width h and in the spectral order p of the method, assuming that the stabilization parameter is O(h/p). For piecewise analytic solutions, exponential convergence is established on quadrilateral meshes. For the DGFEM we admit very general irregular meshes and for the SDFEM we allow meshes which contain hanging nodes. Numerical experiments confirm the theoretical results.Keywords
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