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Estimates for the rate of convergence of finite element approximations of the solution of a time-dependent variational inequality
Bibliography: pages 93-101.
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| Main Author: | |
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| Other Authors: | |
| Format: | Thesis |
| Language: | English |
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Department of Mathematics and Applied Mathematics
2016
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| _version_ | 1867613342322917376 |
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| access_status_str | Open Access |
| author | Schroeder, Gregory C |
| author2 | Reddy, B Daya |
| author_browse | Reddy, B Daya Schroeder, Gregory C |
| author_facet | Reddy, B Daya Schroeder, Gregory C |
| author_sort | Schroeder, Gregory C |
| collection | Thesis |
| description | Bibliography: pages 93-101. |
| format | Thesis |
| id | oai:open.uct.ac.za:11427/17404 |
| institution | University of Cape Town (South Africa) |
| language | eng |
| last_indexed | 2026-06-10T12:34:36.552Z |
| license_str | Not specified — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UCTD — University of Cape Town Open Access Repository |
| publishDate | 2016 |
| publishDateRange | 2016 |
| publishDateSort | 2016 |
| publisher | Department of Mathematics and Applied Mathematics |
| publisherStr | Department of Mathematics and Applied Mathematics |
| record_format | dspace |
| source_str | UCTD — University of Cape Town Open Access Repository |
| spelling | oai:open.uct.ac.za:11427/17404 Estimates for the rate of convergence of finite element approximations of the solution of a time-dependent variational inequality Schroeder, Gregory C Reddy, B Daya Applied Mathematics Bibliography: pages 93-101. 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. 2016-03-01T07:44:15Z 2016-03-01T07:44:15Z 1993 Master Thesis Masters MSc http://hdl.handle.net/11427/17404 eng application/pdf Department of Mathematics and Applied Mathematics Faculty of Science University of Cape Town |
| spellingShingle | Applied Mathematics Schroeder, Gregory C Estimates for the rate of convergence of finite element approximations of the solution of a time-dependent variational inequality |
| thesis_degree_str | Master's |
| title | Estimates for the rate of convergence of finite element approximations of the solution of a time-dependent variational inequality |
| title_full | Estimates for the rate of convergence of finite element approximations of the solution of a time-dependent variational inequality |
| title_fullStr | Estimates for the rate of convergence of finite element approximations of the solution of a time-dependent variational inequality |
| title_full_unstemmed | Estimates for the rate of convergence of finite element approximations of the solution of a time-dependent variational inequality |
| title_short | Estimates for the rate of convergence of finite element approximations of the solution of a time-dependent variational inequality |
| title_sort | estimates for the rate of convergence of finite element approximations of the solution of a time dependent variational inequality |
| topic | Applied Mathematics |
| url | http://hdl.handle.net/11427/17404 |
| work_keys_str_mv | AT schroedergregoryc estimatesfortherateofconvergenceoffiniteelementapproximationsofthesolutionofatimedependentvariationalinequality |