The Finite Element Method: Theory, Implementation, and Applications
By: by Mats G. Larson, Fredrik Bengzon
Contributors: Bengzon, Fredrik; SpringerLink (Online service)
Series: Texts in Computational Science and Engineering -- 10
Publisher: Springer Berlin Heidelberg; Imprint: Springer
Published: 2013
Place of publication: Berlin, Heidelberg
Language: eng
Format: [electronic resource] /
Number of pages: 385
ISBN-13: 9783642332876
Subjects: Computational Mathematics and Numerical Analysis; Partial Differential equations; Computer-Aided Engineering (CAD, CAE) and Design; Computer-aided design; Computer science; Theoretical and Applied Mechanics; Applied Mechanics; Mathematics; Computational Science and Engineering
Description: 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.​
Table of contents: title: 1. Piecewise Polynomial Approximation in 1D; title: 2. The Finite Element Method in 1D; title: 3. Piecewise Polynomial Approximation in 2D; title: 4. The Finite Element Method in 2D; title: 5. Time-dependent Problems; title: 6. Solving Large Sparse Linear Systems; title: 7. Abstract Finite Element Analysis; title: 8. The Finite Element; title: 9. Non-linear Problems; title: 10. Transport Problems; title: 11. Solid Mechanics; title: 12. Fluid Mechanics; title: 13. Electromagnetics; title: 14. Discontinuous Galerkin Methods; title: A. Some Additional Matlab Code; title: References.