Abstract
In [1] Babuška proposed perturbed variational methods for elliptic problems, with discontinuous coefficients. However, these methods are not quasioptimal, i.e. the approximate solutions generated by such methods do not reproduce the properties of “best approximation” possessed by the subspace of admissable approximants. In this paper we consider certain extrapolates obtained by use of a particular method of [1] and obtain “optimal” asymptotic error estimates. Our approach is similar to that of [7] where we proposed extrapolation methods for elliptic problems with smooth coefficients.
Zusammenfassung
In [1] hat Babuška gestörte Variationsmethoden für elliptische Probleme mit unstetigen Koeffizienten vorgeschlagen. Diese Methoden sind aber nicht quasioptimal, d.h. Näherungslösungen, welche durch solche Verfahren erzeugt werden, haben nicht mehr die „beste Approximationseigenschaft” der Elemente des Unterraums der zulässigen Näherungen. In dieser Arbeit betrachten wir gewisse Extrapolaten, welche vermittels einer in [1] angegebenen Methode erhalten werden. Wir erhalten „optimale” asymptotische Fehlerabschätzungen. Unsere Methodik ist ähnlich derer, die wir in [7] gebrauchten, um Extrapolationsmethoden für elliptische Probleme mit glatten Koeffizienten zu erhalten.
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King, J.T. A quasioptimal finite element method for elliptic interface problems. Computing 15, 127–135 (1975). https://doi.org/10.1007/BF02252861
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DOI: https://doi.org/10.1007/BF02252861