Finite Elements: Theory and Algorithms (Cambridge IISc Series)

Written in easy to understand language, this self-explanatory guide introduces the fundamentals of finite element methods and its application to differential equations. Beginning with a brief introduction to Sobolev spaces and elliptic scalar problems, the text progresses through an explanation of finite element spaces and estimates for the interpolation error. The concepts of finite element methods for parabolic scalar parabolic problems, object-oriented finite element algorithms, efficient implementation techniques, and high dimensional parabolic problems are presented in different chapters. Recent advances in finite element methods, including non-conforming finite elements for boundary value problems of higher order and approaches for solving differential equations in high dimensional domains are explained for the benefit of the reader. Numerous solved examples and mathematical theorems are interspersed throughout the text for enhanced learning.

Sashikumaar Ganesan obtained his Ph.D. from Otto-von-Guericke-Universität Magdeburg, Germany 2006. He was Postdoctoral Fellow at Otto-von-Guericke-Universität Magdeburg, Germany (2006–08) and Research Associate (2008–09) at the Imperial College of Science, Technology and Medicine, London. He joined the Indian Institute of Science (IISc), Bangalore as Assistant Professor in 2011. He is currently heading a research group on Numerical Mathematics and Scientific Computing at Supercomputer Education and Research Centre, IISc, Bangalore. His areas of interest include numerical analysis, finite elements in fluid dynamics and high performance computing.

Lutz Tobiska is Professor at the Institute for Analysis and Computational Mathematics, Otto-von-Guericke-Universität Magdeburg, Germany. He received his Ph.D. from the Technische Hochschule Magdeburg in 1977. He has published many articles in international journals. His areas of interest include finite elements in fluid dynamics, parallel algorithms, multigrid methods and adaptive methods for convection diffusion equations.