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dc.contributor.advisor Riviere, Beatrice M.
dc.creatorSardar, Shirin
dc.date.accessioned 2013-03-08T00:38:36Z
dc.date.available 2013-03-08T00:38:36Z
dc.date.issued 2012
dc.identifier.urihttps://hdl.handle.net/1911/70430
dc.description.abstract This thesis formulates and analyzes low-order penalty-free discontinuous Galerkin methods for solving the incompressible Stokes and Navier-Stokes equations. Some symmetric and non-symmetric discontinuous Galerkin methods for incompressible Stokes and Navier-Stokes equations require penalizing jump terms for stability and convergence of the methods. These discontinuous Galerkin methods are called interior penalty methods as the penalizing jump terms involve a penalty parameter. It is known that the penalty parameter has to be large enough to prove coercivity of the bilinear form and therefore to obtain existence of the solution for the symmetric case. The momentum equation is satisfied locally on each mesh element, and it depends on the penalty parameter. Setting the penalty parameter equal to zero yields a singular linear system, if piecewise linears are used. To overcome this instability, this thesis discusses an enrichment of the velocity space with locally supported quadratic functions called bubbles. First, the penalty-free non-symmetric discontinuous Galerkin method is analyzed for the Stokes equations. Second, the main contribution of this thesis is the analysis of both symmetric and non-symmetric penalty-free discontinuous Galerkin methods for the incompressible Varier-Stokes equations. Since a direct application of the generalized Lax-Milgram theorem is not possible, the numerical solution is shown to be the solution as a fixed-point of a problem-related map. A priori error estimate is derived.
dc.format.extent 98 p.
dc.format.mimetype application/pdf
dc.language.iso eng
dc.subjectApplied sciences
Applied mathematics
dc.title Penalty-Free Discontinuous Galerkin Methods for the Stokes and Navier-Stokes Equations
dc.identifier.digital SardarS
dc.type.genre Thesis
dc.type.material Text
thesis.degree.department Computational and Applied Mathematics
thesis.degree.discipline Engineering
thesis.degree.grantor Rice University
thesis.degree.level Masters
thesis.degree.name Master of Arts
dc.identifier.citation Sardar, Shirin. "Penalty-Free Discontinuous Galerkin Methods for the Stokes and Navier-Stokes Equations." (2012) Master’s Thesis, Rice University. https://hdl.handle.net/1911/70430.


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