ABSTRACT

This book covers finite element methods for several typical eigenvalues that arise from science and engineering. Both theory and implementation are covered in depth at the graduate level. The background for typical eigenvalue problems is included along with functional analysis tools, finite element discretization methods, convergence analysis, techniques for matrix evaluation problems, and computer implementation. The book also presents new methods, such as the discontinuous Galerkin method, and new problems, such as the transmission eigenvalue problem.

chapter |34 pages

Functional Analysis

chapter |24 pages

Finite Elements

chapter |24 pages

The Laplace Eigenvalue Problem

chapter |66 pages

The Biharmonic Eigenvalue Problem

chapter |36 pages

The Maxwell's Eigenvalue Problem

chapter |62 pages

The Transmission Eigenvalue Problem

chapter |16 pages

The Schrödinger Eigenvalue Problem

chapter |12 pages

Adaptive Finite Element Approximations

chapter |12 pages

Matrix Eigenvalue Problems

chapter |36 pages

Integral Based Eigensolvers