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Multigrid methods for problems with a small parameter in the highest derivative

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Numerical Analysis

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1066))

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References

  1. ALCOUFFE, R.E., A. BRANDT, J.E. DENDY Jr. & J.W. PAINTER, The multigrid method for the diffusion equation with strongly discontinuous coefficients, SIAM J.S.S.C. 2 (1981) 430–454.

    MathSciNet  MATH  Google Scholar 

  2. ASSELT, E.J. van, The multigrid method and artificial viscosity, In [9], pp. 313–326

    Chapter  Google Scholar 

  3. AXELSSON, O., L.S. FRANK & A. van der SLUIS, Analytical and Numerical Approaches to Asymptotic Problems in Analysis, North-Holland Publ. Comp., Amsterdam-New York, 1981.

    MATH  Google Scholar 

  4. BÖRGERS, C., Mehrgitterverfahren für eine Mehrstellendiskretisierung der Poissongleichung und für eine zweidimensionale singulär gestörte Aufgabe, Diplomarbeit, Institut für Angewandte Mathematik, Universität Bonn, 1981.

    Google Scholar 

  5. BRANDT, A., Multigrid solvers for non-elliptic and singular perturbation steady-state problems, Research Report, Dept. of Applied Mathematics, Weizmann Institute of Science, Rehovot, Israel, 1981.

    Google Scholar 

  6. BRANDT, A., Numerical stability and fast solutions to boundary value problems, In [18],, pp. 29–49.

    MATH  Google Scholar 

  7. BROOKS, A.N. & T.J.R. HUGHES, Streamline-Upwind Petrov-Galerkin Formulations for Convection Dominated Flows with Particular Emphasis on the Incompressible Navier-Stokes Equations, Comp. Meth. Appl. Mech. Engng. 32 (1982) pp. 199–259.

    Article  MathSciNet  MATH  Google Scholar 

  8. HACKBUSCH, W., On the convergence of a multigrid iteration applied to finite element equations, Report 77–8, Inst. Angew. Math., Univ. Köln, 1977.

    Google Scholar 

  9. HACKBUSCH, W. & U. TROTTENBERG (eds), Multigrid Methods, Lecture Notes in Mathematics 960, Springer-Verlag, Berlin, Heidelberg, New York, 1982.

    Google Scholar 

  10. HEMKER, P.W., On the comparison of line-Gauss-Seidel and ILU relaxation in multigrid algorithms, In: J.J.H. Miller (ed.), Computational and asymptotic methods for boundary and interior layers, pp. 269–277. Boole Press, Dublin, 1982.

    Google Scholar 

  11. HEMKER, P.W., Numerical aspects of singular perturbation problems, In: Asymptotic Analysis II (F. Verhulst ed.) Springer LNM 985, pp. 267–287, 1983.

    Google Scholar 

  12. HEMKER, P.W., R. KETTLER, P. WESSELING & P.M. de ZEEUW, Multigrid methods: development of fast solvers, To appear in: Applied Mathematics and Computation.

    Google Scholar 

  13. HEMKER, P.W. & J.J.H. MILLER (eds), Numerical Analysis of Singular Perturbation problems, Academic Press, London, 1979.

    Google Scholar 

  14. JOHNSON, C. & U. NÄVERT, Analysis of some finite element methods for advection-diffusion problems, In [3],, pp. 99–116.

    MATH  Google Scholar 

  15. KETTLER, R., Analysis and comparison of relaxation schemes in robust multigrid and preconditioned conjugate gradient methods, In [9],, pp. 502–534.

    MATH  Google Scholar 

  16. KETTLER, R. & J.A. MEIJERINK, A multigrid method and a combined multigrid conjugate gradient method for elliptic problems with strongly discontinuous coefficients in general domains, KSEPL Publication 604, Kon. Shell Expl. and Prod. Lab., Rijswijk, The Netherlands, 1981.

    Google Scholar 

  17. MEIJERINK, J.A. & H.A. van der VORST, An iterative solution method for linear systems of which the coefficient matrix is a symmetric M-matrix. Math. Comp. 31, 148–162, 1977.

    MathSciNet  MATH  Google Scholar 

  18. MILLER, J.J.H. (ed.), Boundary and Interior Layers-Computational and Asymptotic Methods, Boole Press, Dublin, 1980.

    Google Scholar 

  19. STÜBEN, K. & U. TROTTENBERG, Multigrid Methods: Fundamental Algorithms, Model Problem Analysis and Applications. In [9],, pp. 1–176.

    Book  MATH  Google Scholar 

  20. WESSELING, P., Theoretical and practical aspects of a multigrid method. SIAM J.S.S.C. 3 (1982) 387–407.

    MathSciNet  MATH  Google Scholar 

  21. WESSELING, P., A robust and efficient multigrid method. In [9],, pp. 614–630.

    Book  MATH  Google Scholar 

  22. DE ZEEUW, P.M. & E.J. van ASSELT, The convergence rate of multi-level algorithms applied to the convection-diffusion equations. Report NW 142/82, Mathematical Center, Amsterdam, 1982.

    MATH  Google Scholar 

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Authors
  1. P. W. Hemker
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David F. Griffiths

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© 1984 Springer-Verlag

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Hemker, P.W. (1984). Multigrid methods for problems with a small parameter in the highest derivative. In: Griffiths, D.F. (eds) Numerical Analysis. Lecture Notes in Mathematics, vol 1066. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0099520

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  • DOI: https://doi.org/10.1007/BFb0099520

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-13344-5

  • Online ISBN: 978-3-540-38881-4

  • eBook Packages: Springer Book Archive

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