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A multi-grid continuation strategy for parameter-dependent variational inequalities

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Continuation Techniques and Bifurcation Problems

Abstract

For parameter-dependent nonlinear elliptic obstacle problems a path-following multi-grid continuation strategy is developed combining a nested iteration type scheme as predictor with a subsequent multi-grid method as corrector. The performance of the algorithm is illustrated by some numerical results for the Bratu problem.

Supported in part by the Air Force Office of Scientific Research under grant AFOSR-84-0315.

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References

  1. A. Brandt, Multi-level adaptive solutions to boundary-value problems, Math. Comp. 31 (1977) 333–390.

    Article  Google Scholar 

  2. A. Brandt and C.W. Cryer, Multi-grid algorithms for the solution of linear complementarity problems arising from free boundary problems, SIAM J. Sci. Stat. Comput. 4 (1983) 655–684.

    Article  Google Scholar 

  3. F. Conrad, F. Issard-Roch, C.-M. Brauner and B. Nicolaenko, Nonlinear eigenvalue problems in elliptic variational inequalities: A local study, Comm. Partial Differential Equations 10 (1985) 151–190.

    Article  Google Scholar 

  4. R. Glowinski, J.L. Lions and R. Trémolières, Numerical Analysis of Variational Inequalities (North-Holland, Amsterdam, 1981).

    Google Scholar 

  5. W. Hackbusch, Multi-grid solution of continuation problems, in: R. Ansorge, T. Meis and W. Törnig, Eds., Iterative Solution of Nonlinear Systems, Lecture Notes in Math. 953 (Springer, Berlin, 1982).

    Google Scholar 

  6. W. Hackbusch and H.D. Mittelmann, On multi-grid methods for variational inequalities, Numer. Math. 49 (1983) 239–254.

    Google Scholar 

  7. R.H.W. Hoppe, On the numerical solution of variational inequalities by multi-grid techniques, in: B. Karasözen et al., Eds., Proc. Internat. Symp. on Numerical Analysis, Ankara, Turkey, September 1987 (Plenum Press, New York, to appear).

    Google Scholar 

  8. R.H.W. Hoppe and R. Kornhuber, Multi-grid solution of the two-phase Stefan problem, in: S. McCormick, Ed., Proc. 3rd Copper Mountain Confer, on Multigrid Methods, Copper Mountain, Colorado, April 6–10, 1987 (Marcel Dekker, New York, 1988).

    Google Scholar 

  9. E. Miersemann and H.D. Mittelmann, Continuation for parametrized nonlinear variational inequalities, J. Comput. Appl Math. 26(1&2) (1989) 23–34 (this issue).

    Article  Google Scholar 

  10. H.D. Mittelmann, On continuation for variational inequalities, SIAM J. Numer. Anal. 24 (1987) 1374–1381.

    Article  Google Scholar 

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Hoppe, R.H.W., Mittelmann, H.D. (1990). A multi-grid continuation strategy for parameter-dependent variational inequalities. In: Mittelmann, H.D., Roose, D. (eds) Continuation Techniques and Bifurcation Problems. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série internationale d’Analyse numérique, vol 92. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-5681-2_3

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  • DOI: https://doi.org/10.1007/978-3-0348-5681-2_3

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-7643-2397-4

  • Online ISBN: 978-3-0348-5681-2

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