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Finite Element Methods for Maxwell's Equations$
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Peter Monk

Print publication date: 2003

Print ISBN-13: 9780198508885

Published to Oxford Scholarship Online: September 2007

DOI: 10.1093/acprof:oso/9780198508885.001.0001

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Sobolev Spaces, Vector Function Spaces and Regularity

Sobolev Spaces, Vector Function Spaces and Regularity

(p.36) 3 Sobolev Spaces, Vector Function Spaces and Regularity
Finite Element Methods for Maxwell's Equations

Peter Monk

Oxford University Press

This chapter presents the basic functional analysis and abstract error estimates used in the book. A summary of the relevant theory of linear variational problems,compactness, and the Fredholm alternative is presented. This is followed by a more detailed discussion, with proofs, of the corresponding error estimates including Cea’s lemma, Babuska-Brezzi theory for mixed problems, and convergence theory for collectively compact operators. The Hilbert-Schmidt theory of eigenvalues and error estimates for eigenvalues are also briefly mentioned.

Keywords:   variational problem, Fredholm alternative, Babuska-Brezzi, collectively compact operators, Hilbert-Schmidt theory, eigenvalues

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