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dc.contributor.advisorKirby, Robert C.
dc.creatorKernell, Oliver Tate, 1990-
dc.date.accessioned2019-12-04T16:49:17Z
dc.date.available2019-12-04T16:49:17Z
dc.date.created2019-08
dc.date.issued2019-07-24
dc.date.submittedAugust 2019
dc.identifier.urihttps://hdl.handle.net/2104/10780
dc.description.abstractWe describe finite element methods for the linearized rotating shallow water equations which govern tides. Symplectic Euler and Crank-Nicolson time-stepping strategies have good energy preservation properties, which is desirable for tide modeling, but require careful treatment of linear algebra. For symplectic Euler, we have to invert the Raviart-Thomas element mass matrix at every time step. Thus we give estimates for the eigenvalues of these mass matrices. Crank-Nicolson, being fully implicit, has a more complicated system of equations which requires inverting the entire system. For this, we present an effective block preconditioner using parameter-weighted norms in H(div). We give results that are nearly dependent of the given constants. Finally, we provide numerical results that confirm this theory.
dc.format.mimetypeapplication/pdf
dc.language.isoen
dc.subjectFinite elements. Mixed methods. Preconditioning. Tide model. Rotating shallow water equations.
dc.titlePreconditioning mixed finite elements for tide models.
dc.typeThesis
dc.rights.accessrightsWorldwide access
dc.type.materialtext
thesis.degree.namePh.D.
thesis.degree.departmentBaylor University. Dept. of Mathematics.
thesis.degree.grantorBaylor University
thesis.degree.levelDoctoral
dc.date.updated2019-12-04T16:49:17Z
dc.creator.orcid0000-0003-0816-7027


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