Variational Problems in Weighted Sobolev Spaces with Applications to Computational Fluid Dynamics
Author/Creator
Date
2008-08-19Type of Work
application/pdfText
dissertations
Department
Mathematics and StatisticsProgram
Mathematics, AppliedRights
This item may be protected under Title 17 of the U.S. Copyright Law. It is made available by UMBC for non-commercial research and education. For permission to publish or reproduce, please see http://aok.lib.umbc.edu/specoll/repro.php or contact Special Collections at speccoll(at)umbc.edu.Access limited to the UMBC community. Item may possibly be obtained via Interlibrary Loan through a local library, pending author/copyright holder's permission.
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