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Issues related to least-squares finite element methods for the stokes equations

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dc.contributorVirginia Techen
dc.contributor.authorDeang, Jennifer M.en
dc.contributor.authorGunzburger, Max D.en
dc.date.accessed2014-05-27en
dc.date.accessioned2014-05-28T18:35:09Zen
dc.date.available2014-05-28T18:35:09Zen
dc.date.issued1998-10en
dc.description.abstractLeast-squares finite element methods have become increasingly popular for the approximate solution of first-order systems of partial differential equations. Here, after a brief review of some existing theories, a number of issues connected with the use of such methods for the velocity-vorticity-pressure formulation of the Stokes equations in two dimensions in realistic settings are studied through a series of computational experiments. Finite element spaces that are not covered by existing theories are considered; included in these are piecewise linear approximations for the velocity. Mixed boundary conditions, which are also not covered by existing theories, are also considered, as is enhancing mass conservation. Next, problems in nonconvex polygonal regions and the resulting nonsmooth solutions are considered with a view toward seeing how accuracy can be improved. A conclusion that can be drawn from this series of computational experiments is that the use of appropriate mesh-dependent weights in the least-squares functional almost always improves the accuracy of the approximations. Concluding remarks concerning three-dimensional problems, the nonlinear Navier-Stokes equations, and the conditioning of the discrete systems are provided.en
dc.description.sponsorshipAir Force Office of Scientific Research grant AFOSR-93-1-0280en
dc.format.mimetypeapplication/pdfen
dc.identifier.citationDeang, J. M.; Gunzburger, M. D., "Issues related to least-squares finite element methods for the stokes equations," SIAM J. Sci. Comput., 20(3), 878-906, (1998). DOI: 10.1137/s1064827595294526en
dc.identifier.doihttps://doi.org/10.1137/s1064827595294526en
dc.identifier.issn1064-8275en
dc.identifier.urihttp://hdl.handle.net/10919/48158en
dc.identifier.urlhttp://epubs.siam.org/doi/abs/10.1137/S1064827595294526en
dc.language.isoen_USen
dc.publisherSiam Publicationsen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectleast squaresen
dc.subjectfinite element methodsen
dc.subjectstokes equationsen
dc.subjectpartial-differential equationsen
dc.subjectconjugate-gradient solutionen
dc.subject1st-orderen
dc.subjectelliptic-systemsen
dc.subjectfluid-dynamicsen
dc.subject3 dimensionsen
dc.subjectformulationen
dc.subjectconvergenceen
dc.subjectaccuracyen
dc.subjectmathematics, applieden
dc.titleIssues related to least-squares finite element methods for the stokes equationsen
dc.title.serialSiam Journal on Scientific Computingen
dc.typeArticle - Refereeden
dc.type.dcmitypeTexten

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