Mixed finite element methods for the Stokes and Navier -Stokes equations
Abstract
This dissertation focuses on the development, analysis, and implementation of numerical methods for both steady and unsteady incompressible Stokes and Navier-Stokes equations. Unlike existing methods based on the velocity-pressure formulation, I investigate a new, accurate, robust, and highly efficient numerical methods based on a novel pseudostress-velocity formulation. The well-posedness of the systems is established and error bonds for both time and space discretization are obtained. The pseudostress and the velocity are approximated by a stable pair of finite elements: Raviart-Thomas (RT) elements of index k ≥ 0 and discontinuous piecewise polynomials of degree k ≥ 0, respectively. The pseudostress system from the discretization is solved by the H(div) type of multigrid method, and the velocity is then calculated explicitly. Some numerical examples and comparison are presented too.
Degree
Ph.D.
Advisors
Cai, Purdue University.
Subject Area
Mathematics
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