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A two-grid analysis of the combination of mixed finite elements and Vanka-type relaxation

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Abstract

In this paper a two-grid algorithm is discussed for the mixed finite element discretization of Poisson’s equation. The algorithm is based on a Vanka-type relaxation; the grid transfer operators are selected in accordance with the discretization. Local mode analysis is used to show that Vanka-type relaxation is an efficient smoother indeed. By studying the Fourier transform of the error amplification matrix we find that the canonical grid transfer operators are sufficiently accurate for grid independent convergence. However, this conclusion depends on the relaxation pattern used.

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References

  1. Molenaar, J., and P.W. Hemker (1990). A multigrid approach for the solution of the 2D semiconductor equations, IMPACT, to appear.

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  2. Vanka, S.P. (1986). Block-Implicit Multigrid Solution of Navier-Stokes Equations in Primitive Variables, J. Comput. Phys., 65, 138–158.

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  3. Polak, S.J. W.H.A. Schilders and H.D. Couperus (1988). A finite element method with current conservation, in Simulation of Semiconductor Devices and Processes, Vol. 3, Bologna, Techno-print.

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  4. Brandt, A. (1982). Guide to multigrid development, in Multigrid Methods, Springer Verlag, Lecture Notes in Mathematics 960.

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  5. Hemker, P.W. (1990). On the order of prolongations and restrictions in multigrid procedures, J. Appl. Math., to appear.

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Authors and Affiliations

  1. Centre for Mathematics and Computer Science, P.O. Box 4079, 1009, AB Amsterdam, The Netherlands

    J. Molenaar

Authors
  1. J. Molenaar
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Editors and Affiliations

  1. Institut für Informatik und Praktische Mathematik, Universität Kiel, Olshausenstrasse 40, D-2300, Kiel 1, Germany

    W. Hackbusch

  2. Gesellschaft für Mathematik und Datenverarbeitung mbH, Postfach 1240, Schloss Birlinghoven, D-5205, Sankt Augustin 1, Germany

    U. Trottenberg

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© 1991 Springer Basel AG

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Molenaar, J. (1991). A two-grid analysis of the combination of mixed finite elements and Vanka-type relaxation. In: Hackbusch, W., Trottenberg, U. (eds) Multigrid Methods III. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série Internationale d’Analyse Numérique, vol 98. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-5712-3_23

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  • DOI: https://doi.org/10.1007/978-3-0348-5712-3_23

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-5714-7

  • Online ISBN: 978-3-0348-5712-3

  • eBook Packages: Springer Book Archive

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