Abstract
A finite element method for approximating elliptic equations on domains with corners is proposed. The method makes use of the singular functions of the problem in the trial space and the kernel functions of the adjoint problem in the test space. This leads to good approximates of the coefficients of the singular functions. In the numerical computations, the method is compared with the well known Singular Function Method.
Zusammenfassung
Es wird eine Finite Elemente Methode zur Approximation elliptischer Differentialgleichungen auf Eckengebieten vorgeschlagen. Das Verfahren benutzt die Singulärfunktionen des Problems im Raum der Ansatzfunktionen und die Kernfunktionen des adjungierten Operators im Testraum. Dadurch erhält man gute Näherungen der Koeffizienten, der Singulärfunktionen. In einem numerischen Beispiel wird das Verfahren mit der bekannten Methode der Singulärfunktionen verglichen.
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This work has been supported by the SFB 72 of the Deutsche Forschungsgemeinschaft (DFG).
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Blum, H., Dobrowolski, M. On finite element methods for elliptic equations on domains with corners. Computing 28, 53–63 (1982). https://doi.org/10.1007/BF02237995
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DOI: https://doi.org/10.1007/BF02237995