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Multilevel Methods in Finite Elements

Part of the Lecture Notes in Mathematics book series (LNMCIME,volume 1825)

Abstract

This survey consists of five parts. In the first section we describe a model problem and a two-level algorithm in order to motivate the multilevel approach. In Section 2 an abstract multilevel algorithm is described and analyzed under some regularity assumptions. An analysis under less stringent assumptions is given in Section 3. Non-nested spaces and varying forms are treated in Section 4. Finally, we show how the multilevel framework provides computationally efficient realizations of norms on Sobolev scales.

Keywords

  • Sobolev Space
  • Domain Decomposition
  • Multigrid Method
  • Extension Operator
  • Nodal Basis

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© 2003 Springer-Verlag Berlin Heidelberg

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Bramble, J.H. (2003). Multilevel Methods in Finite Elements. In: Canuto, C. (eds) Multiscale Problems and Methods in Numerical Simulations. Lecture Notes in Mathematics, vol 1825. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-39810-3_3

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  • DOI: https://doi.org/10.1007/978-3-540-39810-3_3

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-20099-4

  • Online ISBN: 978-3-540-39810-3

  • eBook Packages: Springer Book Archive