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Finite element approximation of eigenvalue problems

Published online by Cambridge University Press:  10 May 2010

Daniele Boffi
Daniele Boffi
Affiliation:
Dipartimento di Matematica, Università di Pavia, via Ferrata 1, 27100 Pavia, Italy, E-mail: daniele.boffi@unipv.it
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We discuss the finite element approximation of eigenvalue problems associated with compact operators. While the main emphasis is on symmetric problems, some comments are present for non-self-adjoint operators as well. The topics covered include standard Galerkin approximations, non-conforming approximations, and approximation of eigenvalue problems in mixed form. Some applications of the theory are presented and, in particular, the approximation of the Maxwell eigenvalue problem is discussed in detail. The final part tries to introduce the reader to the fascinating setting of differential forms and homological techniques with the description of the Hodge–Laplace eigenvalue problem and its mixed equivalent formulations. Several examples and numerical computations complete the paper, ranging from very basic exercises to more significant applications of the developed theory.

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Research Article
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Acta Numerica , Volume 19 , May 2010 , pp. 1 - 120
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Copyright © Cambridge University Press 2010

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