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A new streamline diffusion finite element method for the generalized Oseen problem. (English) Zbl 1382.65422

Summary: This paper aims to present a new streamline diffusion method with low order rectangular Bernardi-Raugel elements to solve the generalized Oseen equations. With the help of the Bramble-Hilbert lemma, the optimal errors of the velocity and pressure are estimated, which are independent of the considered parameter \(\varepsilon\). With an interpolation postprocessing approach, the superconvergent error of the pressure is obtained. Finally, a numerical experiment is carried out to confirm the theoretical results.

MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
76M10 Finite element methods applied to problems in fluid mechanics
65N15 Error bounds for boundary value problems involving PDEs
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