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Finite Elements


Theory and Algorithms

Author : Sashikumaar Ganesan & Lutz Tobiska

Availability : In Stock

Format : Hardback

ISBN : 9781108415705

₹ 495.00


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Finite element method (FEM) is a numerical technique for approximation of the solution of partial differential equations. This book on FEM and related simulation tools starts with a brief introduction to Sobolev spaces and elliptic scalar problems and continues with explanation of finite element spaces and estimates for the interpolation error. Construction of finite elements on simplices, quadrilaterals, hexahedral is discussed by the authors in self-contained manner. The last chapter focuses on object-oriented finite element algorithms and efficient implementation techniques. Readers can also find the concepts of scalar parabolic problems and high dimensional parabolic problems in different chapters. Besides, the book includes some recent advances in FEM, including nonconforming finite elements for boundary value problems of higher order and approaches for solving differential equations in high-dimensional domains. There are plenty of solved examples and mathematical theorems interspersed throughout the text for better understanding.

1. Introduction to Sobolev Spaces
2. Elliptic scalar problems
3. Finite element spaces
4. Interpolation and discretization error
5. Biharmonic equation
6. Parabolic problems
7. Systems in solid mechanics
8. Systems in fluid mechanics
9. Implementation of the finite element method
Bibliography
Index

Sashikumaar Ganesan
Author
Sashikumaar Ganesan is Assistant Professor at the Indian Institute of Science (IISc). He heads the research group on Computational Mathematics at the Department of Computational and Data Sciences at IISc. His areas of interest include numerical analysis, finite elements in fluid dynamics, moving boundary value problems, numerical methods for turbulent flows, variational multiscale methods, population balance modelling, scalable algorithms and high performance computing.

Lutz Tobiska
Author
Lutz Tobiska is Professor at the Institute for Analysis and Computational Mathematics, Otto-von-Guericke University Magdeburg, Germany. His research interests include finite elements in fluid dynamics, parallel algorithms, multigrid methods and adaptive methods for convection diffusion equations.