Adaptive finite element methods for linear-quadratic convection dominated elliptic optimal control problems

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dc.contributor.advisorHeinkenschloss, Matthiasen_US
dc.creatorNederkoorn, Eelcoen_US
dc.date.accessioned2011-07-25T02:04:48Zen_US
dc.date.available2011-07-25T02:04:48Zen_US
dc.date.issued2010en_US
dc.description.abstractThe numerical solution of linear-quadratic elliptic optimal control problems requires the solution of a coupled system of elliptic partial differential equations (PDEs), consisting of the so-called state PDE, the adjoint PDE and an algebraic equation. Adaptive finite element methods (AFEMs) attempt to locally refine a base mesh in such a way that the solution error is minimized for a given discretization size. This is particularly important for the solution of convection dominated problems where inner and boundary layers in the solutions to the PDEs need to be sufficiently resolved to ensure that the solution of the discretized optimal control problem is a good approximation of the true solution. This thesis reviews several AFEMs based on energy norm based error estimates for single convection dominated PDEs and extends them to the solution of the coupled system of convection dominated PDEs arising from the optimality conditions for optimal control problems. Keywords Adaptive finite element methods, optimal control problems, convection-diffusion equations, local refinement, error estimation.en_US
dc.format.mimetypeapplication/pdfen_US
dc.identifier.callnoTHESIS MATH.SCI. 2010 NEDERKOORNen_US
dc.identifier.citationNederkoorn, Eelco. "Adaptive finite element methods for linear-quadratic convection dominated elliptic optimal control problems." (2010) Master’s Thesis, Rice University. <a href="https://hdl.handle.net/1911/61980">https://hdl.handle.net/1911/61980</a>.en_US
dc.identifier.urihttps://hdl.handle.net/1911/61980en_US
dc.language.isoengen_US
dc.rightsCopyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.en_US
dc.subjectApplied mathematicsen_US
dc.titleAdaptive finite element methods for linear-quadratic convection dominated elliptic optimal control problemsen_US
dc.typeThesisen_US
dc.type.materialTexten_US
thesis.degree.departmentMathematical Sciencesen_US
thesis.degree.disciplineEngineeringen_US
thesis.degree.grantorRice Universityen_US
thesis.degree.levelMastersen_US
thesis.degree.nameMaster of Artsen_US
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