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ADI-methods for nonlinear variational inequalities of evolution

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Iterative Solution of Nonlinear Systems of Equations

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 953))

Abstract

ADI-iteration is an efficient a means for solving nonlinear systems that occur as conservative discretization schemes for variational inequalities of evolution.

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6. References

  1. Alt, H.W., Luckhaus, S.: Quasi-linear elliptic-parabolic differential equations. Sonderforschungsbereich 123, Preprint 136, Heidelberg, 1982.

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  2. Hornung, U.: A unilateral boundary value problem for unsteady waterflow in porous media. Gorenflo, R., Hoffmann, K.H. (Eds.): "Variational Methods and Ill-Posed Problems". Bibliographisches Institut (1982).

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  3. Hornung, U.: Convergence of the transversal line method for a parabolic-elliptic equation. To appear.

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  4. Hornung, U.: A weak existence theorem for nonlinear diffusion problems. To appear.

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  5. Hornung, U., Messing, W.: Simulation of two-dimensional saturated/unsaturated flows with an exact water balance. Verruijt, A., Barends, F.B.J. (Eds.): "Flow and Transport in Porous Media". Proceedings of EUROMECH 143/Delft. Balkema, Rotterdam (1981), 91–96.

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  6. Hornung, U., Messing, W.: Truncation errors in the numerical solution of horizontal diffusion in saturated/unsaturated media. Advances in Water Resources (1982).

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  7. Messing, W.: Konvergenz-Ordnung von Diskretisierungsverfahren für nichtlineare parabolisch-elliptische Differentialgleichungen. Dissertation, Münster, 1982.

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  8. Ortega, J.M., Rheinboldt, W.C.: Iterative Solution of Nonlinear Equations in Several Variables. Academic Press (1970).

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  9. Wachspress, E.: Iterative Solution of Elliptic Systems. Prentice Hall (1966).

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Authors
  1. Ulrich Hornung
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Editor information

Rainer Ansorge Theodor Meis Willi Törnig

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© 1982 Springer-Verlag

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Hornung, U. (1982). ADI-methods for nonlinear variational inequalities of evolution. In: Ansorge, R., Meis, T., Törnig, W. (eds) Iterative Solution of Nonlinear Systems of Equations. Lecture Notes in Mathematics, vol 953. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0069379

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  • DOI: https://doi.org/10.1007/BFb0069379

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-11602-8

  • Online ISBN: 978-3-540-39379-5

  • eBook Packages: Springer Book Archive

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