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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

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

Peter Monk

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198508885.003.0003

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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