Convergence and stability of two-level penalty mixed finite element method for stationary Navier-Stokes equations

Abstract

The two-level penalty mixed finite element method for the stationary Navier-Stokes equations based on Taylor-Hood element is considered in this paper. Two algorithms are proposed and analyzed. Moreover, the optimal stability analysis and error estimate for these two algorithms are provided. Finally, the numerical tests confirm the theoretical results of the presented algorithms.

Keywords

Navier-Stokes equation / penalty mixed finite element method / twolevel strategy / Taylor-Hood element / error estimate / stability analysis

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2014 Higher Education Press and Springer-Verlag Berlin Heidelberg