The purpose of this paper is to propose a new stabilized finite volume element method for the Navier-Stokes problem.
This new method is based on the multiscale enrichment and uses the lowest equal order finite element pairs P1/P1.
The stability and convergence of the optimal order in H1-norm for velocity and L2-norm for pressure are obtained.
Using a dual problem for the Navier-Stokes problem, the convergence of the optimal order in L2-norm for the velocity is obtained. Finally, numerical example confirms the theory analysis and validates the effectiveness of this new method.
This work are supported by the special research program of the Education Department of Shaanxi Province (No. 16JK1537), the NSF of China (Nos 11271298, 11571275).
Wen, J., He, Y. and Zhao, X. (2016), "Analysis of a new stabilized finite volume element method based on multiscale enrichment for the Navier-Stokes problem", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 26 No. 8, pp. 2462-2485. https://doi.org/10.1108/HFF-06-2015-0244Download as .RIS
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