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Numerical Algorithms for Solving Elliptic-Parabolic Problems

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Numerical Mathematics and Advanced Applications

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This paper deals with numerical algorithms for solving elliptic-parabolic problems. An example of such problem is given by the Richards equation for modeling the saturated-unsaturated water flow in porous media. We consider a linear model problem and investigate the convergence of two finite-volume schemes. The first one uses the implicit approximation in the whole domain, and the second scheme is constructed using the splitting method. Results of numerical experiments are also given.

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References

  1. Alt, H.W., Luckhaus, S.: Quasilinear elliptic-parabolic differential equar tions. Math. Z., 183(4), 311–341 (1983)

    MathSciNet  MATH  Google Scholar 

  2. Chen, Z., Ewing, R.: Fully discrete finite element analysis of multiphase flow in groundwater hydrology. SIAM J. Numer. Anal., 34, 2228–2253 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  3. Čiegis, R., Papastavrou, A., Zemitis, A.: Additive splitting methods for elliptic-parabolic problems. Annalli del Universiteta di Ferrara, Sez. VII, Sc. Mat. Vol. XLVI, 291–306 (2000)

    Google Scholar 

  4. Čiegis, Raim., Čiegis, Rem., Zemitis, A.: Parallel numerical methods for the elliptic-parabolic problem, Progress in Industrial Mathematics at ECMI98, B.G.Teubner, Stuttgart, Leipzig, 206–213 (1999)

    Google Scholar 

  5. Eymard, R., Gallouët, T., Gutnic, M., Herbin, R., Hilhorst, D.: Numerical approximation of an elliptic-parabolic equation arising in environment. Comput. Visual Sci., 3, 33–38 (2000)

    Article  MATH  Google Scholar 

  6. Helmig, R.: Multiphase Flow and Transport Processes in the Subserface. Modelling of Hydrosystems. Springer-Verlag (1997)

    Google Scholar 

  7. Hundsdorfer, W.: A note on stability of the Douglas splitting method, CWI Report NM-R9606, Amsterdam, 1996.

    Google Scholar 

  8. Jäger, W., Kačur, J.: Solution of porous medium systems by linear approximation scheme, Numer. Math., 60, pp.407–427 (1991)

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Vilnius Gediminas Technical University, Saulėtekio Str. 11, LT-2040, Vilnius, Lithuania

    Raimondas Čiegis

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  1. Raimondas Čiegis
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Editors and Affiliations

  1. Faculty of Mathematics and Physics Department of Numerical Mathematics, Charles University Prague, Sokolovská 83, 186 75, Praha 8, Czech Republic

    Miloslav Feistauer , Vít Dolejší , Petr Knobloch  & Karel Najzar , ,  & 

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© 2004 Springer-Verlag Berlin Heidelberg

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Čiegis, R. (2004). Numerical Algorithms for Solving Elliptic-Parabolic Problems. In: Feistauer, M., Dolejší, V., Knobloch, P., Najzar, K. (eds) Numerical Mathematics and Advanced Applications. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-18775-9_20

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  • DOI: https://doi.org/10.1007/978-3-642-18775-9_20

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-62288-5

  • Online ISBN: 978-3-642-18775-9

  • eBook Packages: Springer Book Archive

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