Adaptive Finite Elements with Anisotropic Meshes

W. Huang (), L. Kamenski () and J. Lang ()
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W. Huang: University of Kansas, Department of Mathematics
L. Kamenski: University of Kansas, Department of Mathematics
J. Lang: Technische Universität Darmstadt, Graduate School of Computational Engineering, Center of Smart Interfaces, Department of Mathematics

A chapter in Numerical Mathematics and Advanced Applications 2011, 2013, pp 33-42 from Springer

Abstract: Abstract The paper presents a numerical study for the finite element method with anisotropic meshes. We compare the accuracy of the numerical solutions on quasi-uniform, isotropic, and anisotropic meshes for a test problem which combines several difficulties of a corner singularity, a peak, a boundary layer, and a wavefront. Numerical experiment clearly shows the advantage of anisotropic mesh adaptation. The conditioning of the resulting linear equation system is addressed as well. In particular, it is shown that the conditioning with adaptive anisotropic meshes is not as bad as generally assumed.

Keywords: Posteriori Error Estimate; Finite Element Solution; Finite Element Space; Anisotropic Feature; Mesh Adaptation (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-33134-3_4

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DOI: 10.1007/978-3-642-33134-3_4

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