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Locking-free discontinuous Galerkin methods for problems in elasticity, using linear and multilinear approximations
Includes abstract.
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| Format: | Thesis |
| Language: | English |
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Department of Mathematics and Applied Mathematics
2014
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| _version_ | 1867614225876123648 |
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| access_status_str | Open Access |
| author | Grieshaber, B J |
| author2 | Reddy, Daya |
| author_browse | Grieshaber, B J Reddy, Daya |
| author_facet | Reddy, Daya Grieshaber, B J |
| author_sort | Grieshaber, B J |
| collection | Thesis |
| description | Includes abstract. |
| format | Thesis |
| id | oai:open.uct.ac.za:11427/4887 |
| institution | University of Cape Town (South Africa) |
| language | eng |
| last_indexed | 2026-06-10T12:48:40.173Z |
| license_str | Not specified — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UCTD — University of Cape Town Open Access Repository |
| publishDate | 2014 |
| publishDateRange | 2014 |
| publishDateSort | 2014 |
| 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:11427/4887 Locking-free discontinuous Galerkin methods for problems in elasticity, using linear and multilinear approximations Grieshaber, B J Reddy, Daya Mathematics and Applied Mathematics Includes abstract. Includes bibliographical references. With interior penalty discontinuous Galerkin methods well established as locking-free for lowo-rder triangular elements, and thus an effective alternative to the Standard Galerkin method for nearly incompressible materials, substantial numerical evidence in this work shows that this is not the case for quadrilateral elements. Direct comparisons to triangles illustrate the material dependence of three common interior penalty methods for bilinear quadrilaterals, with locking and other manifestations of poor approximations in the near-incompressible regime. To understand this discrepancy with a view to providing a remedy for the problem, an existing convergence analysis for triangles is looked at for possible extension to the case of quadrilaterals. This highlights the need for a suitable interpolant for the error-splitting approach of the proof. To rectify the problem manifesting in the numerical results, a modification to the formulation or elements themselves is necessary, and a preliminary analysis with bilinear elements, assuming the existence of a suitable interpolant with some basic properties, indicates two modifications as potential remedies: edge-term under-integration, and the use of linear rather than multilinear elements. 2014-07-31T08:07:08Z 2014-07-31T08:07:08Z 2013 Doctoral Thesis Doctoral PhD http://hdl.handle.net/11427/4887 eng application/pdf Department of Mathematics and Applied Mathematics Faculty of Science University of Cape Town |
| spellingShingle | Mathematics and Applied Mathematics Grieshaber, B J Locking-free discontinuous Galerkin methods for problems in elasticity, using linear and multilinear approximations |
| thesis_degree_str | Doctoral |
| title | Locking-free discontinuous Galerkin methods for problems in elasticity, using linear and multilinear approximations |
| title_full | Locking-free discontinuous Galerkin methods for problems in elasticity, using linear and multilinear approximations |
| title_fullStr | Locking-free discontinuous Galerkin methods for problems in elasticity, using linear and multilinear approximations |
| title_full_unstemmed | Locking-free discontinuous Galerkin methods for problems in elasticity, using linear and multilinear approximations |
| title_short | Locking-free discontinuous Galerkin methods for problems in elasticity, using linear and multilinear approximations |
| title_sort | locking free discontinuous galerkin methods for problems in elasticity using linear and multilinear approximations |
| topic | Mathematics and Applied Mathematics |
| url | http://hdl.handle.net/11427/4887 |
| work_keys_str_mv | AT grieshaberbj lockingfreediscontinuousgalerkinmethodsforproblemsinelasticityusinglinearandmultilinearapproximations |