Mathematical foundation of the finite element method

Author: Wang Lieheng
Publisher:
Publish Date: 2004-12-01
Features: This book is one of the series "Graduate Texts in Chinese Academy of Sciences." It is developed based on the lecture notes the author has prepared over the past ten years for graduate students at the Chinese Academy of Sciences Graduate School, Peking University, and University of Science and Technology of China (Hefei). The book attempts to provide a relatively complete mathematical foundation for the finite element method, including variational principles, Sobolev spaces, elliptic boundary value problems, finite element discretization, error analysis of conforming finite element methods, numerical integration effects, isoparametric finite elements, nonconforming finite elements, mixed finite element methods, multigrid methods, multilevel methods, and domain decomposition methods. The book is comprehensive in content, rich in material, and presents theories in an accessible manner using as elementary methods as possible. It is suitable for graduate students and senior undergraduate students in computational mathematics and applied mathematics at universities and colleges, as well as for engineers interested in mathematical theory.