Variational Problems in Weighted Sobolev Spaces with Applications to Computational Fluid Dynamics
Date
2008-08-19Type of Work
application/pdfText
dissertations
Department
Mathematics and StatisticsProgram
Mathematics, AppliedRights
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Subjects
Mathematics (0405)Mathematics (0405)
Poisson problem
Helmholtz problem
Corner singularities
Weighted Sobolev spaces
Navier-Stokes equations
Abstract
We study variational problems in weighted Sobolev spaces on bounded domains with angular points. The specific forms of these variational formulations are motivated by, and applied to, a finite element scheme for the time-dependent Navier-Stokes equations. Specifically, we introduce new variational formulations for the Poisson and Helmholtz problems in what would be a weighted counterpart of H<sup>2