Estimates for the rate of convergence of finite element approximations of the solution of a time-dependent variational inequality

 

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dc.contributor.advisor Reddy, B Daya en_ZA
dc.contributor.author Schroeder, Gregory C en_ZA
dc.date.accessioned 2016-03-01T07:44:15Z
dc.date.available 2016-03-01T07:44:15Z
dc.date.issued 1993 en_ZA
dc.identifier.citation Schroeder, G. 1993. Estimates for the rate of convergence of finite element approximations of the solution of a time-dependent variational inequality. University of Cape Town. en_ZA
dc.identifier.uri http://hdl.handle.net/11427/17404
dc.description Bibliography: pages 93-101. en_ZA
dc.description.abstract The main aim of this thesis is to analyse two types of general finite element approximations to the solution of a time-dependent variational inequality. The two types of approximations considered are the following: 1. Semi-discrete approximations, in which only the spatial domain is discretised by finite elements; 2. fully discrete approximations, in which the spatial domain is again discretised by finite elements and, in addition, the time domain is discretised and the time-derivatives appearing in the variational inequality are approximated by backward differences. Estimates of the error inherent in the above two types of approximations, in suitable Sobolev norms, are obtained; in particular, these estimates express the rate of convergence of successive finite element approximations to the solution of the variational inequality in terms of element size h and, where appropriate, in terms of the time step size k. In addition, the above analysis is preceded by related results concerning the existence and uniqueness of the solution to the variational inequality and is followed by an application in elastoplasticity theory. en_ZA
dc.language.iso eng en_ZA
dc.subject.other Applied Mathematics en_ZA
dc.title Estimates for the rate of convergence of finite element approximations of the solution of a time-dependent variational inequality en_ZA
dc.type Master Thesis
uct.type.publication Research en_ZA
uct.type.resource Thesis en_ZA
dc.publisher.institution University of Cape Town
dc.publisher.faculty Faculty of Science en_ZA
dc.publisher.department Department of Mathematics and Applied Mathematics en_ZA
dc.type.qualificationlevel Masters
dc.type.qualificationname MSc en_ZA
uct.type.filetype Text
uct.type.filetype Image
dc.identifier.apacitation Schroeder, G. C. (1993). <i>Estimates for the rate of convergence of finite element approximations of the solution of a time-dependent variational inequality</i>. (Thesis). University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics. Retrieved from http://hdl.handle.net/11427/17404 en_ZA
dc.identifier.chicagocitation Schroeder, Gregory C. <i>"Estimates for the rate of convergence of finite element approximations of the solution of a time-dependent variational inequality."</i> Thesis., University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 1993. http://hdl.handle.net/11427/17404 en_ZA
dc.identifier.vancouvercitation Schroeder GC. Estimates for the rate of convergence of finite element approximations of the solution of a time-dependent variational inequality. [Thesis]. University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 1993 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/17404 en_ZA
dc.identifier.ris TY - Thesis / Dissertation AU - Schroeder, Gregory C AB - The main aim of this thesis is to analyse two types of general finite element approximations to the solution of a time-dependent variational inequality. The two types of approximations considered are the following: 1. Semi-discrete approximations, in which only the spatial domain is discretised by finite elements; 2. fully discrete approximations, in which the spatial domain is again discretised by finite elements and, in addition, the time domain is discretised and the time-derivatives appearing in the variational inequality are approximated by backward differences. Estimates of the error inherent in the above two types of approximations, in suitable Sobolev norms, are obtained; in particular, these estimates express the rate of convergence of successive finite element approximations to the solution of the variational inequality in terms of element size h and, where appropriate, in terms of the time step size k. In addition, the above analysis is preceded by related results concerning the existence and uniqueness of the solution to the variational inequality and is followed by an application in elastoplasticity theory. DA - 1993 DB - OpenUCT DP - University of Cape Town LK - https://open.uct.ac.za PB - University of Cape Town PY - 1993 T1 - Estimates for the rate of convergence of finite element approximations of the solution of a time-dependent variational inequality TI - Estimates for the rate of convergence of finite element approximations of the solution of a time-dependent variational inequality UR - http://hdl.handle.net/11427/17404 ER - en_ZA


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