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.
"Overall the book is well written […] the authors have done well in balancing the topics based
on their admitted criteria of being either fundamental and appropriate to illustrate
theory or of their own research interests. I highly recommend the book, especially for
the curious graduate student."
—Joe Coyle, Mathematical Reviews, September 2017
Introduction of Eigenvalue Problems. Preliminaries. Finite Elements. The Laplacian Eigenvalue Problems. The Maxwell’s Eigenvalue Problems. The Bi-Harmonic and Quad-Curl Eigenvalue Problems. Eigenvalue Problems of Schrödinger Operator. The Transmission Eigenvalue Problems. Techniques for Matrix Eigenvalue Problems. Appendix.