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Theorie Und Numerik Elliptischer Differentialgleichungen by Wolfgang Hackbusch

Theorie Und Numerik Elliptischer Differentialgleichungen

by Wolfgang Hackbusch
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Book cover type: Paperback
  • ISBN13: 9783658153571
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Springer Spektrum
  • Publisher Imprint: Springer Spektrum
  • Publication Date:
  • Pages: 400
  • Original Price: EUR 28.03
  • Language: German
  • Edition: 4., Uberarb. Au
  • Item Weight: 658 grams
  • BISAC Subject(s): Differential Equations / General

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. Au erdem wurden die vollständigen Lösungen der Übungsaufgaben hinzugefügt.

Prof. Dr. Dr. h.c. Wolfgang Hackbusch, Max-Planck-Institut für Mathematik in den Naturwissenschaften, Leipzig

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