Locking-free discontinuous Galerkin methods for problems in elasticity, using linear and multilinear approximations

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dc.contributor.advisorReddy, Dayaen_ZA
dc.contributor.authorGrieshaber, B Jen_ZA
dc.date.accessioned2014-07-31T08:07:08Z
dc.date.available2014-07-31T08:07:08Z
dc.date.issued2013en_ZA
dc.descriptionIncludes abstract.
dc.descriptionIncludes bibliographical references.
dc.description.abstractWith 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.en_ZA
dc.identifier.apacitationGrieshaber, B. J. (2013). <i>Locking-free discontinuous Galerkin methods for problems in elasticity, using linear and multilinear approximations</i>. (Thesis). University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics. Retrieved from http://hdl.handle.net/11427/4887en_ZA
dc.identifier.chicagocitationGrieshaber, B J. <i>"Locking-free discontinuous Galerkin methods for problems in elasticity, using linear and multilinear approximations."</i> Thesis., University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 2013. http://hdl.handle.net/11427/4887en_ZA
dc.identifier.citationGrieshaber, B. 2013. Locking-free discontinuous Galerkin methods for problems in elasticity, using linear and multilinear approximations. University of Cape Town.en_ZA
dc.identifier.ris TY - Thesis / Dissertation AU - Grieshaber, B J AB - 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. DA - 2013 DB - OpenUCT DP - University of Cape Town LK - https://open.uct.ac.za PB - University of Cape Town PY - 2013 T1 - Locking-free discontinuous Galerkin methods for problems in elasticity, using linear and multilinear approximations TI - Locking-free discontinuous Galerkin methods for problems in elasticity, using linear and multilinear approximations UR - http://hdl.handle.net/11427/4887 ER - en_ZA
dc.identifier.urihttp://hdl.handle.net/11427/4887
dc.identifier.vancouvercitationGrieshaber BJ. Locking-free discontinuous Galerkin methods for problems in elasticity, using linear and multilinear approximations. [Thesis]. University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 2013 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/4887en_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.otherMathematics and Applied Mathematicsen_ZA
dc.titleLocking-free discontinuous Galerkin methods for problems in elasticity, using linear and multilinear approximationsen_ZA
dc.typeDoctoral Thesis
dc.type.qualificationlevelDoctoral
dc.type.qualificationnamePhDen_ZA
uct.type.filetypeText
uct.type.filetypeImage
uct.type.publicationResearchen_ZA
uct.type.resourceThesisen_ZA
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