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Defect correction for nonlinear elliptic difference equations. (English) Zbl 0597.65076

The paper is concerned with the study of a high-order defect correction technique for discretizations of nonlinear elliptic boundary value problems. The convergence of the method is analyzed in general and, in more detail, for a specific example. The algorithmic combination of defect correction and multigrid techniques is also discussed.

MSC:

65N22 Numerical solution of discretized equations for boundary value problems involving PDEs
35J65 Nonlinear boundary value problems for linear elliptic equations
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References:

[1] Auzinger, W.: Defect corrections for multigrid solutions of the Dirichlet problem in general domains. Math. Comput. 1987 (to appear) · Zbl 0615.65102
[2] Auzinger, W., Stetter, H.J.: Defect corrections and multigrid iterations. Lect. Notes Math., vol. 960, pp. 327-351. Berlin, Heidelberg, New York: Springer 1982 · Zbl 0505.65039
[3] Brandt, A.: Multigrid methods: 1984 Guide with applications to fluid dynamics. Arbeitspapiere der GMD, no. 85, St. Augustin, Germany 1984 · Zbl 0581.76033
[4] Hackbusch, W.: Multi-grid methods and applications. Springer Series in Computational Mathematics, vol. 4. Berlin, Heidelberg, New York, Tokyo: Springer 1985 · Zbl 0595.65106
[5] Hackbusch, W.: On multigrid iterations with defect corrections. Lect. Notes Math., vol. 960, pp. 461-473. Berlin, Heidelberg, New York: Springer 1982
[6] Stetter, H.J.: The defect correction principle and discretization methods. Numer. Math.29, 425-443 (1978) · Zbl 0362.65052 · doi:10.1007/BF01432879
[7] Stüben, K., Trottenberg, U.: Multigrid methods: Fundamental algorithms, model problem analysis and applications. Lect. Notes Math., vol. 960, pp. 1-176. Berlin, Heidelberg, New York: Springer 1982 · Zbl 0562.65071
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