Stabilized finite element method for Navier–Stokes equations with physical boundary conditions

Amara, M.; Capatina-Papaghiuc, D.; Trujillo, D.

doi:10.1090/S0025-5718-07-01929-1

Stabilized finite element method for Navier–Stokes equations with physical boundary conditions
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by M. Amara, D. Capatina-Papaghiuc and D. Trujillo PDF

Math. Comp. 76 (2007), 1195-1217 Request permission

Abstract:

This paper deals with the numerical approximation of the 2D and 3D Navier-Stokes equations, satisfying nonstandard boundary conditions. This lays on the finite element discretisation of the corresponding Stokes problem, which is achieved through a three-fields stabilized mixed formulation. A priori and a posteriori error bounds are established for the nonlinear problem, ascertaining the convergence of the method. Finally, numerical tests are presented, including mesh refinement via error indicators.

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