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- W588889644 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 H2 ∩ H10 , show the existence and uniqueness of solutions, and establish the relationship with the traditional H1 formulations. We formulate a conforming C 1 finite element method for solving these variational problems and prove its convergence. We apply our methods to the time-dependent Navier-Stokes equations on non-convex polygonal domains by adapting an iterative algorithm due to Liu, Liu, and Pego. The well-posedness of the modified algorithm follows from our analysis of the Poisson and Helmholtz problems. Numerical results for several benchmark problems are provided." @default.
- W588889644 created "2016-06-24" @default.
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- W588889644 date "2008-01-01" @default.
- W588889644 modified "2023-10-18" @default.
- W588889644 title "Variational problems in weighted sobolev spaces with applications to computational fluid dynamics" @default.
- W588889644 hasPublicationYear "2008" @default.
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