Error identities for variational problems with obstacles

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F60076658%3A12310%2F18%3A43897558" target="_blank" >RIV/60076658:12310/18:43897558 - isvavai.cz</a>
Alternative codes found
RIV/67985556:_____/18:00483574
Result on the web
<a href="https://onlinelibrary.wiley.com/doi/epdf/10.1002/zamm.201700105" target="_blank" >https://onlinelibrary.wiley.com/doi/epdf/10.1002/zamm.201700105</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1002/zamm.201700105" target="_blank" >10.1002/zamm.201700105</a>

Result language
angličtina
Original language name
Error identities for variational problems with obstacles
Original language description
The paper is devoted to analysis of a class of nonlinear free boundary problems that are usually solved by variational methods based on primal, dual or primal-dual variational settings. We deduce and investigate special relations (error identities). They show that a certain nonlinear measure of the distance to the exact solution (specific for each problem) is equivalent to the respective duality gap, whose minimization is the keystone of all variational numerical methods. Therefore, the identity actually sets the measure that contains maximal quantitative information on the quality of a numerical solution available through these methods. The measure has quadratic terms generated by the linear part of the differential operator and nonlinear terms associated with the free boundary. We obtain fully computable two sided bounds of this measure and show that they provide efficient estimates of the distance between the minimizer and any function (approximation) from the corresponding energy space. Several computational examples show that for different minimization sequences the balance between the quadratic and the nonlinear terms of the overall error measure may be different and essential contribution of nonlinear terms may serve as an indicator that the free boundaries are approximated very roughly.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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