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dc.contributor.advisorDavid L. Darmofal.en_US
dc.contributor.authorCouchman, Benjamin Luke Streatfielden_US
dc.contributor.otherMassachusetts Institute of Technology. Department of Aeronautics and Astronautics.en_US
dc.date.accessioned2018-05-23T16:30:13Z
dc.date.available2018-05-23T16:30:13Z
dc.date.copyright2018en_US
dc.date.issued2018en_US
dc.identifier.urihttp://hdl.handle.net/1721.1/115685
dc.descriptionThesis: S.M., Massachusetts Institute of Technology, Department of Aeronautics and Astronautics, 2018.en_US
dc.descriptionCataloged from PDF version of thesis.en_US
dc.descriptionIncludes bibliographical references (pages 77-79).en_US
dc.description.abstractThe ability to handle discontinuities appropriately is essential when solving nonlinear hyperbolic partial differential equations (PDEs). Discrete solutions to the PDE must converge to weak solutions in order for the discontinuity propagation speed to be correct. As shown by the Lax-Wendroff theorem, one method to guarantee that convergence, if it occurs, will be to a weak solution is to use a discretely conservative scheme. However, discrete conservation is not a strict requirement for convergence to a weak solution. This suggests a hierarchy of discretizations, where discretely conservative schemes are a subset of the larger class of methods that converge to the weak solution. We show here that a range of finite element methods converge to the weak solution without using discrete conservation arguments. The effect of using quadrature rules to approximate integrals is also considered. In addition, we show that solutions using non-conservation working variables also converge to weak solutions.en_US
dc.description.statementofresponsibilityby Benjamin Luke Streatfield Couchman.en_US
dc.format.extent79 pagesen_US
dc.language.isoengen_US
dc.publisherMassachusetts Institute of Technologyen_US
dc.rightsMIT theses are protected by copyright. They may be viewed, downloaded, or printed from this source but further reproduction or distribution in any format is prohibited without written permission.en_US
dc.rights.urihttp://dspace.mit.edu/handle/1721.1/7582en_US
dc.subjectAeronautics and Astronautics.en_US
dc.titleOn the convergence of higher-order finite element methods to weak solutionsen_US
dc.typeThesisen_US
dc.description.degreeS.M.en_US
dc.contributor.departmentMassachusetts Institute of Technology. Department of Aeronautics and Astronautics
dc.identifier.oclc1036985680en_US


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