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Local projection stabilization for the Oseen problem and its interpretation as a variational multiscale method. (English) Zbl 1109.35086

Summary: We propose to apply the recently introduced local projection stabilization to the numerical computation of the Oseen equation at high Reynolds number. The discretization is done by nested finite element spaces. Using a priori error estimation techniques, we prove the convergence of the method. The a priori estimates are independent of the local Peclet number and give a sufficient condition for the size of the stabilization parameters in order to ensure optimality of the approximation when the exact solution is smooth. Moreover, we show how this method may be cast in the framework of variational multiscale methods. We indicate what modeling assumptions must be made to use the method for large eddy simulations.

MSC:

35Q30 Navier-Stokes equations
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
76M10 Finite element methods applied to problems in fluid mechanics
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
76D05 Navier-Stokes equations for incompressible viscous fluids
76F65 Direct numerical and large eddy simulation of turbulence
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