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Discrete Energy Laws for the First-Order System Least-Squares Finite-Element Approach Read chapter Read first chapter

2018 | OriginalPaper | Chapter

Verifications of Primal Energy Identities for Variational Problems with Obstacles

Authors : Sergey Repin, Jan Valdman

Published in: Large-Scale Scientific Computing

Publisher: Springer International Publishing

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Abstract

We discuss error identities for two classes of free boundary problems generated by obstacles. The identities suggest true forms of the respective error measures which consist of two parts: standard energy norm and a certain nonlinear measure. The latter measure controls (in a weak sense) approximation of free boundaries. Numerical tests confirm sharpness of error identities and show that in different examples one or another part of the error measure may be dominant.

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previous chapter On a Problem of Optimal Control of Convection-Diffusion Processes
next chapter An Optimal Control Problem with a Risk Zone
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Repin, S.: A posteriori error estimation for variational problems with uniformly convex functionals. Math. Comput. 69(230), 481–500 (2000)MathSciNetCrossRefMATH
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Repin, S., Valdman, J.: Error identities for variational problems with obstacles. ZAMM (in print)
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Shahgholian, H., Uraltseva, N.N., Weiss, G.S.: The two-phase membrane problem regularity of the free boundaries in higher dimensions. Int. Math. Res. Not. 2007(8), ID rnm026 (2007)
Metadata
Title
Verifications of Primal Energy Identities for Variational Problems with Obstacles
Authors
Sergey Repin
Jan Valdman
Copyright Year
2018
Book
Large-Scale Scientific Computing

Print ISBN: 978-3-319-73440-8

Electronic ISBN: 978-3-319-73441-5

Copyright Year: 2018

DOI
https://doi.org/10.1007/978-3-319-73441-5_18

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