The Finite Element Method: Theory, Impleme...

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Sprache: Englisch

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Beschreibung

This book gives an introduction to the finite element method as a general computational method for solving partial differential equations approximately. Our approach is mathematical in nature with a strong focus on the underlying mathematical principles, such as approximation properties of piecewise polynomial spaces, and variational formulations of partial differential equations, but with a minimum level of advanced mathematical machinery from functional analysis and partial differential equations. In principle, the material should be accessible to students with only knowledge of calculus of several variables, basic partial differential equations, and linear algebra, as the necessary concepts from more advanced analysis are introduced when needed. Throughout the text we emphasize implementation of the involved algorithms, and have therefore mixed mathematical theory with concrete computer code using the numerical software MATLAB is and its PDE-Toolbox. We have also had the ambition to cover some of the most important applications of finite elements and the basic finite element methods developed for those applications, including diffusion and transport phenomena, solid and fluid mechanics, and also electromagnetics.¿

Zusammenfassung

Introduction to finite elements only based on calculus and linear algebra

Covers theory, implementation and applications. Focus on basic mathematical principles and consequent use of the same approach in different applications

Matlab programs included

Wide range of applications including solid mechanics, electromagnetics, and fluid mechanics

Covers modern topics such as adaptivity based on duality arguments?

Includes supplementary material: [...]

Inhaltsverzeichnis

1. Piecewise Polynomial Approximation in 1D.- 2. The Finite Element Method in 1D.- 3. Piecewise Polynomial Approximation in 2D.- 4. The Finite Element Method in 2D.- 5. Time-dependent Problems.- 6. Solving Large Sparse Linear Systems.- 7. Abstract Finite Element Analysis.- 8. The Finite Element.- 9. Non-linear Problems.- 10. Transport Problems.- 11. Solid Mechanics.- 12. Fluid Mechanics.- 13. Electromagnetics.- 14. Discontinuous Galerkin Methods.- A. Some Additional Matlab Code.- References.

Details

Erscheinungsjahr:	2015
Fachbereich:	EDV
Genre:	Informatik
Rubrik:	Naturwissenschaften & Technik
Thema:	Lexika
Medium:	Taschenbuch
Seiten:	416
Reihe:	Texts in Computational Science and Engineering
Inhalt:	xvii 395 S.
ISBN-13:	9783642447112
ISBN-10:	3642447112
Sprache:	Englisch
Ausstattung / Beilage:	Paperback
Einband:	Kartoniert / Broschiert
Autor:	Bengzon, Fredrik Larson, Mats G.
Auflage:	2013
Hersteller:	Springer Berlin Springer Berlin Heidelberg Texts in Computational Science and Engineering
Maße:	235 x 155 x 23 mm
Von/Mit:	Fredrik Bengzon (u. a.)
Erscheinungsdatum:	25.06.2015
Gewicht:	0,628 kg

preigu-id: 104503192