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The rate of convergence of a multiple grid method

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Numerical Analysis

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 773))

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References

  1. G.P. Astrakhantsev: An iterative method of solving elliptic net problems. USSR Comp. Math. Math. Phys. 11, no.2, 171–182, 1971.

    Article  MATH  Google Scholar 

  2. I. Babuška: Error bounds for finite element method. Num. Math. 16, 322–333 (1971).

    Article  MathSciNet  MATH  Google Scholar 

  3. I. Babuška and A.K. Aziz: Survey lectures on the mathematical foundations of the finite element method. In: A.K. Aziz (ed.): The mathematical foundations of the finite element method with applications to partial differential equations. Academic Press, New York and London, 1972.

    Google Scholar 

  4. N.S. Bakhvalov: On the convergence of a relaxation method with natural constraints on the elliptic operator. USSR Comp. Math. Math. Phys. 6, no. 5, 101–135 (1966).

    Article  MathSciNet  MATH  Google Scholar 

  5. A. Brandt: Multi-level adaptive technique (MIAT) for fast numerical solution to boundary-value problems. Proc. 3rd Internat. Conf. on Numerical Methods in Fluid Mech. (Paris, 1972), Lecture Notes in Physics 180, 82–89, Springer-Verlag, Berlin and New York, 1972.

    Google Scholar 

  6. Brant: Multi-level adaptive solutions to boundary-value problems. Math. Comp. 31, 333–390 (1977).

    Article  MathSciNet  Google Scholar 

  7. R.P. Fedorenko: A relaxation method for solving elliptic difference equations. USSR Comp. Math. Math. Phys. 1, 1092–1096 (1962).

    Article  MATH  Google Scholar 

  8. R.P. Fedorenko: The speed of convergence of one iterative process. USSR Comp. Math. Math. Phys. 4 no. 3, 227–235 (1964).

    Article  MATH  Google Scholar 

  9. P.O. Frederickson: Fast approximate inversion of large sparse linear systems. Mathematics Report 7–75, 1975, Lakehead University.

    Google Scholar 

  10. W. Hackbusch: On the multi-grid method applied to difference equations, Computing 20, 291–306 (1978).

    Article  MathSciNet  MATH  Google Scholar 

  11. W. Hackbusch: Convergence of multi-grid iterations applied to difference equations. Math. Inst., Universität zu Köln, Report 79-5, April 1979.

    Google Scholar 

  12. R.A. Nicolaides: On multiple grid and related techniques for solving discrete elliptic systems. J. Comp. Phys. 19, 418–431 (1975).

    Article  MathSciNet  MATH  Google Scholar 

  13. R.A. Nicolaides: On the l2 convergence of an algorithm for solving finite element equations. Math. Comp. 31, 892–906 (1977).

    MathSciNet  MATH  Google Scholar 

  14. J. Nitsche and J.C.C. Nitsche: Error estimates for the numerical solution of elliptic differential equations. Arch. Rat. Mech. Anal. 5, 293–306 (1960).

    Article  MathSciNet  MATH  Google Scholar 

  15. P. Wesseling: Numerical solution of the stationary Navier-Stokes equations by means of a multiple grid method and Newton iteration. Report NA-18, Delft University of Technology, 1977.

    Google Scholar 

  16. P. Wesseling: A convergence proof for a multiple grid method. Report NA-21, Delft University of Technology, 1978.

    Google Scholar 

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Authors
  1. P. Wesseling
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G. Alistair Watson

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© 1980 Springer-Verlag

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Wesseling, P. (1980). The rate of convergence of a multiple grid method. In: Watson, G.A. (eds) Numerical Analysis. Lecture Notes in Mathematics, vol 773. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0094171

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  • DOI: https://doi.org/10.1007/BFb0094171

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-09740-2

  • Online ISBN: 978-3-540-38562-2

  • eBook Packages: Springer Book Archive

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