The Finite Element Method: Theory, Implementation, and Applications

• Main Authors: Larson, Mats G. (Author), Bengzon, Fredrik. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2013.
• Series: Texts in Computational Science and Engineering, 10
• Subjects: Mathematics.; Computer aided design.; Differential equations, partial.; Computer science > Mathematics.; Computer science.; Mechanics, applied.; Computational Science and Engineering.; Partial Differential Equations.; Theoretical and Applied Mechanics.; Computer-Aided Engineering (CAD, CAE) and Design.; Computational Mathematics and Numerical Analysis.
• Online Access: https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-3-642-33287-6

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...

Table of Contents:

• 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.