A priori error estimates of finite element models of systems of shallow water equations

Simple item page
dc.contributor.advisorWheeler, Mary F.en_US
dc.contributor.advisorDawson, Clint N.en_US
dc.creatorMartinez, Monica Luciaen_US
dc.date.accessioned2009-06-04T06:26:48Zen_US
dc.date.available2009-06-04T06:26:48Zen_US
dc.date.issued1998en_US
dc.description.abstractIn recent years, there has been much interest in the numerical solution of shallow water equations. The numerical procedure used to solve the shallow water equations must resolve the physics of the problem without introducing spurious oscillations or excessive numerical diffusion. Staggered-grid finite difference methods have been used extensively in modeling surface flow without introducing spurious oscillations. Finite element methods, permitting a high degree of grid flexibility for complex geometries and facilitating grid refinement near land boundaries to resolve important processes, have become much more prevalent. However, early finite element simulations of shallow water systems were plagued by spurious oscillations and the various methods introduced to eliminate these oscillations through artificial diffusion were generally unsuccessful due to excessive damping of physical components of the solution. Here, we give a brief overview on some finite element models of the shallow water equations, with particular attention given to the wave and characteristic formulations. In the literature, standard analysis, based on Fourier decompositions of these methods, has always neglected contributions from the nonlinear terms. We derive ${\cal L}\sp{\infty} ((0,T); {\cal L}\sp2(\Omega))$ and ${\cal L}\sp2((0,T); {\cal H}\sp1(\Omega))$ a priori error estimates for both the continuous-time and discrete-time Galerkin approximation to the nonlinear wave model, finding these to be optimal in ${\cal H}\sp1(\Omega).$ Finally, we derive ${\cal L}\sp{\infty}((0,T); {\cal L}\sp2(\Omega))$ and ${\cal L}\sp2((0,T); {\cal H}\sp1(\Omega))$ a priori error estimates for our proposed Characteristic-Galerkin approximation to the nonlinear primitive model. We find these estimates to be optimal in ${\cal H}\sp1(\Omega)$ but with less restrictive time-step constraints when compared to the Galerkin estimates for the wave model.en_US
dc.format.extent106 p.en_US
dc.format.mimetypeapplication/pdfen_US
dc.identifier.callnoTHESIS SP. SCI. 1998 MARTINEZen_US
dc.identifier.citationMartinez, Monica Lucia. "A priori error estimates of finite element models of systems of shallow water equations." (1998) Diss., Rice University. <a href="https://hdl.handle.net/1911/19287">https://hdl.handle.net/1911/19287</a>.en_US
dc.identifier.urihttps://hdl.handle.net/1911/19287en_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.subjectMathematicsen_US
dc.subjectCivil engineeringen_US
dc.subjectOcean engineeringen_US
dc.titleA priori error estimates of finite element models of systems of shallow water equationsen_US
dc.typeThesisen_US
dc.type.materialTexten_US
thesis.degree.departmentSpace Scienceen_US
thesis.degree.disciplineNatural Sciencesen_US
thesis.degree.grantorRice Universityen_US
thesis.degree.levelDoctoralen_US
thesis.degree.nameDoctor of Philosophyen_US
Files
Original bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
9827420.PDF
Size:
3.24 MB
Format:
Adobe Portable Document Format
Download
Collections
Rice University Theses and Dissertations