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＜電子ブック＞
The Finite Element Method: Theory, Implementation, and Applications / by Mats G. Larson, Fredrik Bengzon
(Texts in Computational Science and Engineering. ISSN:2197179X ; 10)

版	1st ed. 2013.
出版者	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
出版年	2013
本文言語	英語
大きさ	XVII, 395 p : online resource
著者標目	*Larson, Mats G author Bengzon, Fredrik author SpringerLink (Online service)
件　名	LCSH:Mathematics -- Data processing  全ての件名で検索 LCSH:Differential equations LCSH:Mechanics, Applied LCSH:Computer-aided engineering FREE:Computational Science and Engineering FREE:Differential Equations FREE:Engineering Mechanics FREE:Computer-Aided Engineering (CAD, CAE) and Design FREE:Computational Mathematics and Numerical Analysis
一般注記	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 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 tocover 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. HTTP:URL=https://doi.org/10.1007/978-3-642-33287-6

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