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Mathematical Modelling and Analysis Volume 9, 2004 - Issue 2
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Original Articles

Monotone and conservative difference schemes for elliptic equations with mixed derivativesFootnote1

I.V. Rybak Institute of Mathematics, National Academy of Sciences of Belarus, 11 Surganov Str., Minsk, 220072, Belams E-mail: [email protected]‐net.by
Pages 169-178 | Received 13 Nov 2003, Published online: 14 Oct 2010

References

  • Arbogast , T. , Wheeler , M.F. and Yotov , I. 1997 . Mixed finite elements for elliptic problems with tensor coefficients as cell‐centered finite differences . SIAMJ.Numer. Anal , 34 (2) : 828 – 852 .
  • Crumpton , P. , Shaw , G. and Ware , A. 1995 . Discretization and multigrid solution of elliptic equations with mixed derivative terms and strongly discontinuous coefficients . J. Comput. Phys , 116 : 343 – 358 .
  • Godunov , S. and Ryabenkii , V. 1973 . Difference schemes Nauka, Moskow (in Russian)
  • Hyman , J. , Morel , J. , Shashkov , M. and Steinberg , S. 2002 . Mimetic finite difference methods for diffusion equations . Computational Geosciences , 6 : 333 – 352 .
  • Samarskii , A. 2001 . The theory of difference schemes , New York‐Basel : Marcel Dekker, Inc. .
  • Samarskii , A. and Andreev , V. 1976 . Difference methods for elliptic equations Nauka, Moskow (in Russian)
  • Samarskii , A. , Matus , P. , Mazhukin , V. and Mozolevski , I. 2002 . Monotone difference schemes for equations with mixed derivatives . Computers and Mathematics with Applications , 44 : 501 – 510 .
  • Samarskii , A. , Mazhukin , V. , Matus , P. and Shishkin , G. 2001 . Monotone difference schemes for equations with mixed derivatives . Mathematical Modeling , 13 (2) : 17 – 26 .
  • Schneider , G. and Zedan , M. 1981 . A modified strongly implicit procedure for the numerical solution of field problems . Numerical Heat Transfer , 4 : 1 – 19 .
  • Shishkin , G. 1992 . “ Grid approximation of the singularly perturbed boundary‐value problem for quasilinear parabolic equations in the case of total degeneracy with respect to space variables ” . In Numerical methods and mathematical modeling , Edited by: Kuznetsov , Yu.A. 103 – 128 . Moskow : Russian Academy of Sciences, Institute of Computational Mathematics .
  • Voligt , W. 1988 . Finite‐difference schemes for parabolic problems with first and mixed second derivatives . Z. angew. Math. und Mech , 68 (7) : 281 – 288 .
  • The author thanks Prof. Oleg Iliev and Prof. Raimondas Čiegis for the statement of the problem, Prof. Piotr Matus and Dr. Mikhail Chuiko for the discussion and useful comments

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