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Incremental unknowns for solving partial differential equations

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Summary

Incremental unknowns have been proposed in [T] as a method to approximate fractal attractors by using finite difference approximations of evolution equations. In the case of linear elliptic problems, the utilization of incremental unknown methods provides a new way for solving such problems using several levels of discretization; the method is similar but different from the classical multigrid method.

In this article we describe the application of incremental unknowns for solving Laplace equations in dimensions one and two. We provide theoretical results concerning two-level approximations and we report on numerical tests done with multi-level approximations.

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References

  • [AB] Axelsson, O., Barker, V.A.: Finite element solution of boundary value problem: Theory and computation. New York: Academic Press 1984

    Google Scholar 

  • [CT] Chen, M., Temam, R.: to appear

  • [FMT] Foias, C., Manley, O., Temam, R.: Sur l'interaction des petits et grands tourbillons dans des écoulements turbulents. C.R. Acad. Sc. Paris, Serie 1,305, 497–500 (1987)

    Google Scholar 

  • Foias, C., Manley, O., Temam, R.: Modelling of the interaction of small and large eddies in two-dimensional turbulent flows. Math. Mod. Numer. Anal. (M2AN)22, 93–114 (1988)

    Google Scholar 

  • [FST] Foias, C., Sell, G.R., Temam, R.: Inertial Manifolds for nonlinear evolutionary equations. J. Diff. Equ.73, 309–353 (1988)

    Google Scholar 

  • [G] Garcia, S.: to appear

  • [H] Hackbusch, W.: Multi-Grid Methods and Applications. Berlin Heidelberg New York: Springer 1985

    Google Scholar 

  • [MT1] Marion, M., Temam, R.: Nonlinear Galerkin Methods. SIAM J. Numer. Anal.26, No. 5, 1139–1157 (1989)

    Google Scholar 

  • [MT2] Marion, M., Temam, R.: Nonlinear Galerkin Methods; The finite elements case. Numer. Math.57, 205–226 (1990)

    Google Scholar 

  • [T] Temam, R.: Inertial manifolds and multigrid methods. SIAM J. Math. Anal.21, No. 1, 154–178 (1990)

    Google Scholar 

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Authors and Affiliations

  1. Institute for Applied Mathematics and Scientific Computing, Indiana University, 618 East Third Street, 47405, Bloomington, IN, USA

    Min Chen & Roger Temam

  2. Laboratoire d'Analyse Numérique, Université de Paris-Sud, Bâtiment 425, F-91405, Orsay Cedex, France

    Roger Temam

Authors
  1. Min Chen
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  2. Roger Temam
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Chen, M., Temam, R. Incremental unknowns for solving partial differential equations. Numer. Math. 59, 255–271 (1991). https://doi.org/10.1007/BF01385779

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  • DOI: https://doi.org/10.1007/BF01385779

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