Abstract
We consider multigrid applied to a class of singularly perturbed two-point boundary value problems. In the multigrid method we use a matrix-dependent prolongation and restriction. For a class of two-grid method we prove uniform convergence for allh (mesh size parameter) and ε (perturbation parameter).
Zusammenfassung
In dieser Arbeit wird ein Mehrgittierverfahren für eine Klasse singulär gestörter Randwertprobleme untersucht. In dem mehrgitterverfahren verwenden wir eine matrixabhängige prolongation und Restriktion. Für eine Klasse von Zweigittermethoden beweisen wir gleichmäßige Konvergenz für alleh (Schrittweitenparameter) und ε (Parameter der singuläre Störung).
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Reusken, A. Multigrid with matrix-dependent transfer operators for a singular perturbation problem. Computing 50, 199–211 (1993). https://doi.org/10.1007/BF02243811
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DOI: https://doi.org/10.1007/BF02243811