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.advisorReddy, B Dayaen_ZA
dc.contributor.authorSchroeder, Gregory Cen_ZA
dc.date.accessioned2016-03-01T07:44:15Z
dc.date.available2016-03-01T07:44:15Z
dc.date.issued1993en_ZA
dc.descriptionBibliography: pages 93-101.en_ZA
dc.description.abstractThe 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.identifier.apacitationSchroeder, 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/11427/17404en_ZA
dc.identifier.chicagocitationSchroeder, 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/11427/17404en_ZA
dc.identifier.citationSchroeder, 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.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
dc.identifier.urihttp://hdl.handle.net/11427/17404
dc.identifier.vancouvercitationSchroeder 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/11427/17404en_ZA
dc.language.isoengen_ZA
dc.publisher.departmentDepartment of Mathematics and Applied Mathematicsen_ZA
dc.publisher.facultyFaculty of Scienceen_ZA
dc.publisher.institutionUniversity of Cape Town
dc.subject.otherApplied Mathematicsen_ZA
dc.titleEstimates for the rate of convergence of finite element approximations of the solution of a time-dependent variational inequalityen_ZA
dc.typeMaster Thesis
dc.type.qualificationlevelMasters
dc.type.qualificationnameMScen_ZA
uct.type.filetypeText
uct.type.filetypeImage
uct.type.publicationResearchen_ZA
uct.type.resourceThesisen_ZA
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