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dc.contributor.advisor Riviere, Beatrice M.
dc.creatorLiu, Kun
dc.date.accessioned 2013-03-08T00:36:03Z
dc.date.available 2013-03-08T00:36:03Z
dc.date.issued 2011
dc.identifier.urihttps://hdl.handle.net/1911/70327
dc.description.abstract This thesis proposes and analyses two numerical methods for solving elliptic partial differential equations with random coefficients. The stochastic problem is first transformed into a parametrized one by the use of the Karhunen--Loève expansion. This new problem is then discretized by the discontinuous Galerkin (DG) method. A priori error estimate in the energy norm for the stochastic discontinuous Galerkin solution is derived. In addition, the expected value of the numerical error is theoretically bounded in the energy norm and the L2 norm. In the second approach, the Monte Carlo method is used to generate independent identically distributed realizations of the stochastic coefficients. The resulting deterministic problems are solved by the DG method. Next, estimates are obtained for the error between the average of these approximate solutions and the expected value of the exact solution. The Monte Carlo discontinuous Galerkin method is tested numerically on several examples. Results show that the nonsymmetric DG method is stable independently of meshes and the value of penalty parameter. Symmetric and incomplete DG methods are stable only when the penalty parameter is large enough. Finally, comparisons with the Monte Carlo finite element method and the Monte Carlo discontinuous Galerkin method are presented for several cases.
dc.format.extent 95 p.
dc.format.mimetype application/pdf
dc.language.iso eng
dc.subjectApplied sciences
Applied mathematics
dc.title Discontinuous Galerkin Methods for Elliptic Partial Differential Equations with Random Coefficients
dc.identifier.digital LiuKun
dc.type.genre Thesis
dc.type.material Text
thesis.degree.department Computational and Applied Mathematics
thesis.degree.discipline Engineering
thesis.degree.grantor Rice University
thesis.degree.level Masters
thesis.degree.name Master of Arts
dc.identifier.citation Liu, Kun. "Discontinuous Galerkin Methods for Elliptic Partial Differential Equations with Random Coefficients." (2011) Master’s Thesis, Rice University. https://hdl.handle.net/1911/70327.


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