Theorie und Numerik elliptischer Differentialgleichungen

Theorie und Numerik elliptischer Differentialgleichungen

Wolfgang Hackbusch

34,96 €
IVA incluido
Disponible
Editorial:
Springer Nature B.V.
Año de edición:
2016
ISBN:
9783658153571
34,96 €
IVA incluido
Disponible

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Das Verständnis der numerischen Behandlung elliptischer Differentialgleichungen erfordert notwendigerweise auch die Kenntnisse der Theorie der Differentialgleichungen. Deshalb behandelt das Buch beide parallel. Zunächst wird der klassische Zugang (starke Lösungen, Differenzenverfahren) beschrieben. Dem Maximum-Minimum-Prinzip auf der theoretischen Seite entsprechen beispielsweise die Eigenschaften der M-Matrizen, die sich bei der Diskretisierung ergeben. Nach einem Exkurs über die Funktionalanalysis werden die Variationsformulierung und die Finite-Element-Diskretisierungen behandelt. Weitere Themen sind die Analyse der Diskretisierungen von Eigenwertaufgaben und die Stokes-Gleichungen mit den inf-sup-Bedingungen für die Finite-Element-Diskretisierung. Auf der theoretischen Seite wird die Regularität der Lösungen näher untersucht.Gegenüber der zweiten Auflage enthält der vorliegende Text zahlreiche Aktualisierungen, vor allem im Bereich der Finiten Elemente sowie in den Literaturangaben. Außerdem wurden die vollständigen Lösungen der Übungsaufgaben hinzugefügt.

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