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Finite Difference Scheme for Filtration and Consolidation Problems

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Numerical Methods and Applications (NMA 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2542))

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Abstract

It’s well known that numerical instabilities appear in the approximation of the Biot's consolidation problem, when standard finite elements or difference methods are applied. To stabilizate this problem, we propose the use of staggered grids for the discretization. A monotone and second order finite difference scheme on this kind of grid is given. We check this properties with some numerical results.

This research has been partially supported by the Spanish project MCYT-FEDER BFM 2001-2521 and The Russian Foundation for Basic Research RFBR 99-01-00958

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Author information

Authors and Affiliations

  1. Departamento de Matemática Aplicada, Universidad de Zaragoza, 50009, Zaragoza, Spain

    Francisco J. Gaspar & Francisco J. Lisbona

  2. Institute for Mathematical Modelling RAS, 4-A, Miusskaya Sq., 124047, Moscow, Russia

    Petr N. Vabishchevich

Authors
  1. Francisco J. Gaspar
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  2. Francisco J. Lisbona
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  3. Petr N. Vabishchevich
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Editor information

Editors and Affiliations

  1. Central Laboratory for Parallel Processing, Bulgarian Academy of Sciences, Acad. G. Bonchev, bl. 25A, 1113, Sofia, Bulgaria

    Ivan Dimov , Ivan Lirkov  & Svetozar Margenov ,  & 

  2. National Environmental Research Institute, Frederiksborgvej 399, P.O. Box 358, 4000, Roskilde, Denmark

    Zahari Zlatev

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© 2003 Springer-Verlag Berlin Heidelberg

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Gaspar, F.J., Lisbona, F.J., Vabishchevich, P.N. (2003). Finite Difference Scheme for Filtration and Consolidation Problems. In: Dimov, I., Lirkov, I., Margenov, S., Zlatev, Z. (eds) Numerical Methods and Applications. NMA 2002. Lecture Notes in Computer Science, vol 2542. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36487-0_51

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  • DOI: https://doi.org/10.1007/3-540-36487-0_51

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-00608-4

  • Online ISBN: 978-3-540-36487-0

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