Numerical Approximation of Partial Differe...

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Beschreibung

Finite element methods for approximating partial differential equations have reached a high degree of maturity, and are an indispensible tool in science and technology. This textbook aims at providing a thorough introduction to the construction, analysis, and implementation of finite element methods for model problems arising in continuum mechanics. The first part of the book discusses elementary properties of linear partial differential equations along with their basic numerical approximation, the functional-analytical framework for rigorously establishing existence of solutions, and the construction and analysis of basic finite element methods. The second part is devoted to the optimal adaptive approximation of singularities and the fast iterative solution of linear systems of equations arising from finite element discretizations. In the third part, the mathematical framework for analyzing and discretizing saddle-point problems is formulated, corresponding finte element methods are analyzed, and particular applications including incompressible elasticity, thin elastic objects, electromagnetism, and fluid mechanics are addressed. The book includes theoretical problems and practical projects for all chapters, and an introduction to the implementation of finite element methods.

Über den Autor

Sören Bartels is Professor of Applied Mathematics
at the Albert-Ludwigs University in Freiburg, Germany. His primary
research interest is in the development and analysis of approximation schemes
for nonlinear partial differential equations with applications in the
simulation of modern materials. Professor Bartels has published the Springer
textbook "Numerik 3x9" and the monograph "Numerical methods for nonlinear
partial differential equations" in the Springer Series in Computational
Mathematics.

Zusammenfassung

Matlab implementations illustrate the devised methods

Problems, projects, and quizzes allow for self-evaluation

Includes theoretical and physical backgrounds of mathematical models

Inhaltsverzeichnis

Preface.- Part I Finite differences and finite elements.- Elliptic partial differential equations.- Finite Element Method.- Part II Local resolution and iterative solution.- Local Resolution Techniques.- Iterative Solution Methods.- Part III Constrained and singularly perturbed problems.- Saddled-point Problems.- Mixed and Nonstandard methods.- Applications.- Problems and Projects.- Implementation aspects.- Notations, inequalities, guidelines.- Index

Details

Erscheinungsjahr:	2018
Fachbereich:	Wahrscheinlichkeitstheorie
Genre:	Mathematik , Medizin , Naturwissenschaften , Technik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Inhalt:	xv 535 S. 170 s/w Illustr. 535 p. 170 illus.
ISBN-13:	9783319812656
ISBN-10:	3319812653
Sprache:	Englisch
Einband:	Kartoniert / Broschiert
Autor:	Bartels, Sören
Auflage:	Softcover reprint of the original 1st edition 2016
Hersteller:	Springer International Publishing
Verantwortliche Person für die EU:	Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße:	235 x 155 x 30 mm
Von/Mit:	Sören Bartels
Erscheinungsdatum:	30.05.2018
Gewicht:	0,826 kg

Artikel-ID: 114236773