The hp Streamline Diffusion Finite Element Method for Convection Dominated Problems in one Space Dimension
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1998-10
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Abstract
We analyze the hp Streamline Diffusion Finite Element Method (SDFEM) and the standard Galerkin FEM for one dimensional stationary convection-diffusion problems. Under the assumption of analyticity of the input data, a mesh is exhibited on which approximation with continuous piecewise polynomials of degree p allows for resolution of the boundary layer. On such meshes, both the SDFEM and the Galerkin FEM lead to robust exponential convergence in the "energy norm" and in the $L^\infty$ norm. Next, we show that even in the case that the boundary layers are not resolved, robust exponential convergence on compact subsets "upstream" of the layer can be achieved with the hp-SDFEM. This is possible on sequences of meshes that would typically be generated by an hp-adaptive scheme. Detailed numerical experiments confirm our convergence estimates.
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1998-10
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Seminar for Applied Mathematics, ETH Zurich
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02501 - Seminar für Angewandte Mathematik / Seminar for Applied Mathematics
03435 - Schwab, Christoph / Schwab, Christoph