Penalty finite element method for the Navier-Stokes equations |
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Authors: | G.F. Carey R. Krishnan |
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Affiliation: | Texas Institute for Computational Mechanics, University of Texas at Austin, Austin, TX 78712, U.S.A. |
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Abstract: | We present an analysis of a penalty formulation of the stationary Navier-Stokes equations for an incompressible fluid. Subject to restrictions on the viscosity and prescribed body force, it is shown that there exists a unique solution to this penalty problem. The solution to the penalty problem is shown to converge to the solution of the Navier-Stokes problem as O(ε) where ε → 0 is the penalty parameter.Existence, uniqueness and stability properties for the approximate problem are then developed and we derive estimates for finite element approximation of the penalized Navier-Stokes problem presented here. Numerical studies are conducted to examine rates of convergence and sample numerical results presented for test cases. |
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