Abstract
We construct a method which makes it possible to apply the idea of iterated defect correction to finite element methods. The construction is motivated heuristically. We believe that the significance of our method lies in the possibility to write “metaalgorithms” for existing finite element program packages which entail a substantial improvement of the accuracy of these program packages. The efficiency of the method is demonstrated in a number of examples.
Zusammenfassung
Wir geben ein Verfahren an, das es ermöglicht, den Gedanken der Iterierten Defektkorrektur auf Methoden der Finiten Elemente anzuwenden. Das Verfahren wird heuristisch motiviert. Wir glauben, daß die Bedeutung unseres Verfahrens in der Möglichkeit liegt, für bestehende Finite-Elemente-Programmpakete „Metaalgorithmen” zu schreiben, die eine beträchtliche Steigerung der Genauigkeit dieser Programmpakete bewirken. Die Effizienz des Verfahrens wird an einigen Beispielen demonstriert.
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Frank, R., Hertling, J. & Monnet, J.P. The application of iterated defect correction to variational methods for elliptic boundary value problems. Computing 30, 121–135 (1983). https://doi.org/10.1007/BF02280783
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DOI: https://doi.org/10.1007/BF02280783