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Adaptive Finite Elements with Anisotropic Meshes

In: Numerical Mathematics and Advanced Applications 2011

Author

Listed:
  • 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)

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.

Suggested Citation

  • W. Huang & L. Kamenski & J. Lang, 2013. "Adaptive Finite Elements with Anisotropic Meshes," Springer Books, in: Andrea Cangiani & Ruslan L. Davidchack & Emmanuil Georgoulis & Alexander N. Gorban & Jeremy Levesley (ed.), Numerical Mathematics and Advanced Applications 2011, edition 127, pages 33-42, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-33134-3_4
    DOI: 10.1007/978-3-642-33134-3_4
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