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Theorie und Numerik elliptischer Differentialgleichungen

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Brand
Springer Nature
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N/A
Part Number
0
GTIN
9783658153571
Condition
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Product Description

Das Verstndnis der numerischen Behandlung elliptischer Differentialgleichungen erfordert notwendigerweise auch die Kenntnisse der Theorie der Differentialgleichungen. Deshalb behandelt das Buch beide parallel. Zunchst wird der klassische Zugang (starke Lsungen, 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 ber 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 fr die Finite-Element-Diskretisierung. Auf der theoretischen Seite wird die Regularitt der Lsungen nher untersucht. Gegenber der zweiten Auflage enthlt der vorliegende Text zahlreiche Aktualisierungen, vor allem im Bereich der Finiten Elemente sowie in den Literaturangaben. Auerdem wurden die vollstndigen Lsungen der bungsaufgaben hinzugefgt.

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