DSpace Repository

A posteriori error analysis and adaptive finite element solution of variational inequalities of the second kind

Show simple item record

dc.contributor.advisor HAN, Weimin
dc.contributor.author BOSTAN, Viorel
dc.date.accessioned 2021-04-06T10:56:59Z
dc.date.available 2021-04-06T10:56:59Z
dc.date.issued 2004
dc.identifier.citation BOSTAN, Viorel. A posteriori error analysis and adaptive finite element solution of variational inequalities of the second kind: tz. requirement for the Doctor of Philosophy degree in Applied Mathematical and Computational Sciences. Th. Supervisor Weimin HAN. Iowa City, IA, USA, 2004. 24 p. en_US
dc.identifier.uri http://repository.utm.md/handle/5014/14028
dc.description Document Preview https://search.proquest.com/openview/398599661d9496b5c5f3221225f30036/1?pq-origsite=gscholar&cbl=18750&diss=y Fişierul ataşat conţine: Information to Users, Acknowledgements, Abstract, Table of Contents, List of Tables, List of Figures, Introduction en_US
dc.description.abstract In the employment of the finite element method (and other numerical methods) for solving application problems, an important issue is to assess the reliability of the numerical solution. A posteriori error estimates provide quantitative information on the accuracy of the numerical solution and are the basis for the development of automatic, adaptive procedures for engineering applications of the finite element method. We perform an a posteriori error analysis for adaptive finite element solution of elliptic variational inequalities of the second kind. Using duality theory in convex analysis, we establish a general framework for a posteriori error estimation. We then derive a posteriori error estimates of residual type and of gradient recovery type, with particular choices of the dual variable present in the general framework. The reliability of the error estimates is rigorously shown. The efficiency of the error estimators is theoretically investigated and numerically validated. Detailed derivation and analysis of the error estimates are given for a model variational inequality of the second kind. We present extension of the results in solving other elliptic variational inequalities such as those arising in the study of frictional contact problems in elasticity. First, we derive a posteriori error estimates for a static frictional contact problem, and then consider a quasistatic case. We report numerous numerical examples, illustrating the effectiveness of the a posteriori error estimates. en_US
dc.language.iso en en_US
dc.rights Attribution-NonCommercial-NoDerivs 3.0 United States *
dc.rights.uri http://creativecommons.org/licenses/by-nc-nd/3.0/us/ *
dc.subject variational inequalities en_US
dc.subject inequalities en_US
dc.title A posteriori error analysis and adaptive finite element solution of variational inequalities of the second kind en_US
dc.type Thesis en_US


Files in this item

The following license files are associated with this item:

This item appears in the following Collection(s)

Show simple item record

Attribution-NonCommercial-NoDerivs 3.0 United States Except where otherwise noted, this item's license is described as Attribution-NonCommercial-NoDerivs 3.0 United States

Search DSpace


Advanced Search

Browse

My Account