Please use this identifier to cite or link to this item: https://hdl.handle.net/10356/50615
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dc.contributor.authorChen, Jieen
dc.date.accessioned2012-08-07T07:33:43Zen
dc.date.available2012-08-07T07:33:43Zen
dc.date.copyright2011en
dc.date.issued2011en
dc.identifier.citationChen, J. (2011). Superconvergence of linear finite elements on simplicial meshes. Doctoral thesis, Nanyang Technological University, Singapore.en
dc.identifier.urihttps://hdl.handle.net/10356/50615en
dc.description.abstractIn this dissertation work, we present a theoretical analysis for linear finite element gradient superconvergence on three-dimensional simplicial meshes where the lengthes of each pair of opposite edges in most tetrahedrons differ only by $O(h^{1+\alpha})$. We first derive a local error expansion formula in $n$ dimensional spaces and then use this identity to analyze the interpolantwise gradient superconvergence on simplicial meshes. In three dimensional spaces, we show that the gradient of the linear finite element solution $u_h$ is superconvergent to the gradient of the linear interpolation $u_I$ with an order $O(h^{1+\rho})(0<\rho\leq \alpha)$. Numerical examples are presented to verify the theoretical result. In four dimensional spaces, we find that there is no simplicial mesh that satisfies the edge pair condition.en
dc.format.extent150 p.en
dc.language.isoenen
dc.subjectDRNTU::Science::Mathematicsen
dc.titleSuperconvergence of linear finite elements on simplicial meshesen
dc.typeThesisen
dc.contributor.supervisorWang Deshengen
dc.contributor.schoolSchool of Physical and Mathematical Sciencesen
dc.description.degreeDOCTOR OF PHILOSOPHY (SPMS)en
dc.identifier.doi10.32657/10356/50615en
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