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Zbl 1129.35004
He, Yinnian; Sun, Weiwei
Stabilized finite element method based on the Crank-Nicolson extrapolation scheme for the time-dependent Navier-Stokes equations.
(English)
[J] Math. Comput. 76, No. 257, 115-136 (2007). ISSN 0025-5718; ISSN 1088-6842/e

A stabilized finite element method with the Crank-Nicolson extrapolation in time is studied theoretically. The method is applied to the incompressible Navier-Stokes equations and the error analysis is presented. For the finite element approximation the Q1-P0 quadrilateral element or the P1-P0 triangle element are used. The viscous and pressure terms are approximated implicitly in time. The nonlinear convection term is approximated semi-implicitly. The authors show, for example, that the $L^\infty(0,T; L^2(\Omega))$ error is of order $O(h^2 + \tau^{3/2}).$
[Mária Lukáčová (Hamburg)]
MSC 2000:
*35A35 Theoretical approximation to solutions of PDE
35Q30 Stokes and Navier-Stokes equations
65N15 Error bounds (BVP of PDE)
65N30 Finite numerical methods (BVP of PDE)
76D06 Statistical solutions of Navier-Stokes and related equations

Keywords: Navier-Stokes problem; stabilized finite element; Crank-Nicolson extrapolation scheme; quadrilateral element; triangle element

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