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Rannacher, Rolf: Numerik 3: Probleme der Kontinuumsmechanik und ihre numerische Behandlung, Heidelberg: Heidelberg University Publishing, 2017. DOI: 10.17885/heiup.312.424

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978-3-946054-63-4 (PDF)

978-3-946054-64-1 (Softcover)

Published 11/16/2017.

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Rolf Rannacher

Numerik 3

Probleme der Kontinuumsmechanik und ihre numerische Behandlung

Lecture Notes

This introductory text is based on courses within a multi-semester cycle on “Numerical Mathematics” given by the author at Heidelberg University over a period of 25 years. The present fourth part is devoted to problems in Continuum Mechanics, especially in Structural and Fluid Mechanics, and their numerical solution by finite element methods. Again theoretical as well as practical aspects are considered. As basis of an appropriate numerical approximation the mathematical models are systematically derived from fundamental physical principles. The understanding of the contents requires besides the material of the preceding parts of this series, “Numerik 0 (Einführung in die Numerische Mathematik)”, “Numerik 1 (Numerik gewöhnlicher Differentialgleichungen)”, and “Numerik 2 (Numerik partieller Differentialgleichungen)” only that prior knowledge as is usually provided in the basic Analysis and Linear Algebra courses.

Rolf Rannacher, retired Professor of Numerical Mathematics at Heidelberg University – study of Mathematics at the University of Frankfurt/Main, doctorate 1974, postdoctorate 1978 at Bonn University – 1979/1980 Vis. Assoc. Professor at the University of Michigan (Ann Arbor, USA), thereafter Professor at Erlangen and Saarbrücken, in Heidelberg since 1988 – field of interest “Numerics of Partial Differential Equations”, especially the “Finite Element Method” and its applications in the Natural Sciences and Engeneering; more than 160 scientific publications.

Contents
PDF
Titelei
Inhalt
Einleitung
Kapitel 1: Kontinuumsmechanische Grundlagen
Kapitel 2: Die Grundgleichungen der Strömungsmechanik
Kapitel 3: Die Grundgleichungen der Strukturmechanik
Kapitel 4: Inkompressible und schwach-kompressible Fluide
Kapitel 5: FE-Methoden in der linearen Elastizität
Kapitel 6: FE-Methoden für inkompressible Strömungen
Kapitel 7: FE-Methoden für kompressible Strömungen
Literaturverzeichnis
Index