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Simplicial finite elements in higher dimensions

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Abstract

Over the past fifty years, finite element methods for the approximation of solutions of partial differential equations (PDEs) have become a powerful and reliable tool. Theoretically, these methods are not restricted to PDEs formulated on physical domains up to dimension three. Although at present there does not seem to be a very high practical demand for finite element methods that use higher dimensional simplicial partitions, there are some advantages in studying the methods independent of the dimension. For instance, it provides additional insights into the structure and essence of proofs of results in one, two and three dimensions. In this survey paper we review some recent progress in this direction.

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Authors and Affiliations

  1. Korteweg-De Vries Institute for Mathematics, Plantage Muidergracht 24, 1018 TV, Amsterdam, The Netherlands

    Jan Brandts

  2. Institute of Mathematics, Helsinki University of Technology, P.O. Box 1100, FIN-02015 TKK, Finland

    Sergey Korotov

  3. Institute of Mathematics of the Academy of Sciences of the Czech Republic, Žitná 25, 115 67, Prague 1, Czech Republic

    Michal Křížek

Authors
  1. Jan Brandts
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  2. Sergey Korotov
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  3. Michal Křížek
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Additional information

The second author was supported by Grant No. 112444 of the Academy of Finland. The third author was supported by grant No. 201/04/1503 of the Grant Agency of the Czech Republic.

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Brandts, J., Korotov, S. & Křížek, M. Simplicial finite elements in higher dimensions. Appl Math 52, 251–265 (2007). https://doi.org/10.1007/s10492-007-0013-6

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  • DOI: https://doi.org/10.1007/s10492-007-0013-6

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