Galerkin Projections Between Finite Element Spaces

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dc.contributor.authorThompson, Ross Anthonyen
dc.contributor.committeechairBorggaard, Jeffrey T.en
dc.contributor.committeememberChung, Matthiasen
dc.contributor.committeememberAdjerid, Slimaneen
dc.contributor.departmentMathematicsen
dc.date.accessioned2015-06-18T08:03:24Zen
dc.date.available2015-06-18T08:03:24Zen
dc.date.issued2015-06-17en
dc.description.abstractAdaptive mesh refinement schemes are used to find accurate low-dimensional approximating spaces when solving elliptic PDEs with Galerkin finite element methods. For nonlinear PDEs, solving the nonlinear problem with Newton's method requires an initial guess of the solution on a refined space, which can be found by interpolating the solution from a previous refinement. Improving the accuracy of the representation of the converged solution computed on a coarse mesh for use as an initial guess on the refined mesh may reduce the number of Newton iterations required for convergence. In this thesis, we present an algorithm to compute an orthogonal L^2 projection between two dimensional finite element spaces constructed from a triangulation of the domain. Furthermore, we present numerical studies that investigate the efficiency of using this algorithm to solve various nonlinear elliptic boundary value problems.en
dc.description.degreeMaster of Scienceen
dc.format.mediumETDen
dc.identifier.othervt_gsexam:5569en
dc.identifier.urihttp://hdl.handle.net/10919/52968en
dc.publisherVirginia Techen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectFinite element methodsen
dc.subjectadaptive mesh refinementen
dc.subjectmulti-mesh interpolationen
dc.titleGalerkin Projections Between Finite Element Spacesen
dc.typeThesisen
thesis.degree.disciplineMathematicsen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.levelmastersen
thesis.degree.nameMaster of Scienceen

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