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Coarse grid spaces for domains with a complicated boundary

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Abstract

It is shown that, with homogeneous Dirichlet boundary conditions, the condition number of finite element discretization matrices remains uniformly bounded independent of the size of the boundary elements provided that the size of the elements increases with their distance to the boundary. This fact allows the construction of simple multigrid methods of optimal complexity for domains of nearly arbitrary shape.

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Authors and Affiliations

  1. Mathematisches Institut der Universität Tübingen, D-72076, Tübingen, Germany

    Harry Yserentant

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  1. Harry Yserentant
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Yserentant, H. Coarse grid spaces for domains with a complicated boundary. Numerical Algorithms 21, 387–392 (1999). https://doi.org/10.1023/A:1019157313043

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  • DOI: https://doi.org/10.1023/A:1019157313043

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