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dc.contributor.advisorAwanou, Gerard
dc.creatorMalitz, Eric M
dc.date.accessioned2019-08-06T14:17:53Z
dc.date.available2019-08-06T14:17:53Z
dc.date.created2019-05
dc.date.issued2019-03-18
dc.date.submittedMay 2019
dc.identifier.urihttp://hdl.handle.net/10027/23693
dc.description.abstractWe consider the C0 interior penalty and mixed finite element approximations of the Monge-Ampère equation with C0 Lagrange elements. We solve the discrete nonlinear system of equations with a two-grid method. This method consists in first solving the nonlinear problem on a coarse grid, and then using that solution as the initial guess for a single Newton iteration on a fine grid. Numerical results demonstrate that the two-grid method is more efficient than Newton's method on the fine grid. We give new proofs of convergence for each discrete problem, and prove the convergence of the two-grid methods with optimal error estimates in each case. We give the first theoretical study of multi-grid methods for finite element discretizations of the Monge-Ampère equation. Finally, we prove convergence of a time marching method for solving the nonlinear system resulting from the C0 interior penalty discretization.
dc.format.mimetypeapplication/pdf
dc.subjectMonge-Ampere equation
dc.subjectpartial differential equations
dc.subjectnumerical methods
dc.subjectfinite element method
dc.subjecttwo-grid method
dc.subjectnonlinear equations
dc.titleTwo-Grid Discretization for Finite Element Approximations of the Elliptic Monge-Ampere Equation
dc.typeThesis
thesis.degree.departmentMathematics, Statistics, and Computer Science
thesis.degree.grantorUniversity of Illinois at Chicago
thesis.degree.levelDoctoral
thesis.degree.namePhD, Doctor of Philosophy
dc.contributor.committeeMemberBona, Jerry
dc.contributor.committeeMemberNicholls, David
dc.contributor.committeeMemberVerschelde, Jan
dc.contributor.committeeMemberLi, Hengguang
dc.type.materialtext
dc.contributor.chairAwanou, Gerard


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