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On Adaptive Grid Refinement in the Presence of Internal or Boundary Layers.

Please always quote using this URN: urn:nbn:de:0297-zib-230
  • We propose an anisotropic refinement strategy which is specially designed for the efficient numerical resolution of internal and boundary layers. This strategy is based on the directed refinement of single triangles together with adaptive multilevel grid orientation. It is demonstrated by several numerical examples that compared to usual methods, the new anisotropic refinement ends up in more stable and more accurate solutions at much less computational cost. {\bf Keywords:} Adaptive finite elements, directed refinement, adaptive grid orientation, convection diffusion equation, internal and boundary layers.

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Author:Ralf Kornhuber, Rainer Roitzsch
Document Type:ZIB-Report
Tag:adaptive finite elements; adaptive grid orientation; convection diffusion equation; directed refinement; internal and boundary layers
MSC-Classification:35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Jxx Elliptic equations and systems [See also 58J10, 58J20] / 35J70 Degenerate elliptic equations
35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Lxx Hyperbolic equations and systems [See also 58J45] / 35L67 Shocks and singularities [See also 58Kxx, 76L05]
65-XX NUMERICAL ANALYSIS / 65Nxx Partial differential equations, boundary value problems / 65N30 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
Date of first Publication:1989/07/03
Series (Serial Number):ZIB-Report (SC-89-05)
Published in:Appeared in: IMPACT Comput. Sci. Engrg. 2 (1990) pp. 40-72
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