Sun Jiguang - Finite element methods for eigenvalue problems

Finite Element
Methods for
Eigenvalue
Problems MONOGRAPHS AND RESEARCH NOTES IN MATHEMATICSSeries Editors John A. Burns
Thomas J. Tucker
Miklos Bona
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Jiguang Sun
Michigan Technological University
Houghton, USA Aihui Zhou
Chinese Academy of Sciences
Beijing, China CRC Press
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The numerical solution of eigenvalue problems is of fundamental importance in many scientific and engineering applications, such as structural dynamics, quantum chemistry, electrical networks, magnetohydrodynamics, and control theory []. Due to the flexibility in treating complex structures and rigorous theoretical justification, finite element methods, including conforming finite elements, nonconforming finite elements, mixed finite elements, discontinuous Galerkin methods, etc., have been popular for eigenvalue problems of partial differential equations. There are many excellent references on finite element methods for eigenvalue problems [].

However, to the authors opinion, there is a need for a self-contained, systematic, and up-to-date treatment. This is the motivation for this book. We start with functional analysis including operator perturbation theory in ], which serves as a major tool for convergence analysis of many eigenvalue problems. We introduce basics of finite element methods in . Again, other than a complete account, we keep the introduction concise and refer the readers to classical textbooks. For example, we only choose the typical triangular mesh in two dimensions and tetrahedral mesh in three dimensions.