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The hp-Version of the Streamline Diffusion Finite Element Method in Two Space Dimensions

by K. Gerdes and j. M. Melenk and D. Schötzau and Ch. Schwab

(Report number 1999-17)

Abstract
The Streamline Diffusion Finite Element Method (SDFEM) for a two dimensional convection-diffusion problem is analyzed in the context of the hp-version of the Finite Element Method (FEM). It is proved that the appropriate choice of the SDFEM parameters leads to stable methods on the class of "boundary layer meshes" which may contain anisotropic needle elements of arbitrarily high aspect ratio. Consistency results show that the use of such meshes can resolve layer components present in the solutions at robust exponential rates of convergence. We confirm these theoretical results in a series of numerical examples.

Keywords: Streamline Diffusion Methods, hp Finite Element Methods

@Techreport{GMSS99_251,
  author = {K. Gerdes and j. M. Melenk and D. Sch\"otzau and Ch. Schwab},
  title = {The hp-Version of the Streamline Diffusion Finite Element Method in Two Space Dimensions},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {1999-17},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports1999/1999-17.pdf },
  year = {1999}
}

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