SPATIAL ERROR ESTIMATES FOR A FINITE ELEMENT VISCOSITY-SPLITTING SCHEME FOR THE NAVIER-STOKES EQUATIONS

被引:0
作者
Guillen-Gonzalez, Francisco [1 ]
Victoria Redondo-Neble, Maria [2 ]
机构
[1] Univ Seville, Dept Ecuac Diferenciales & Anal Numer, E-41080 Seville, Spain
[2] Univ Cadiz, Dept Matemat, Cadiz 11510, Spain
关键词
Navier-Stokes Equations; splitting in time schemes; fully discrete schemes; error estimates; mixed formulation; stable finite elements; APPROXIMATION; GALERKIN;
D O I
暂无
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In this paper, we obtain optimal first order error estimates for a fully discrete fractional-step scheme applied to the Navier-Stokes equations. This scheme uses decomposition of the viscosity in time and finite elements (FE) in space. In [15], optimal first order error estimates (for velocity and pressure) for the corresponding time-discrete scheme were obtained, using in particular H-2 x H-1 estimates for the approximations of the velocity and pressure. Now, we use this time-discrete scheme as an auxiliary problem to study a fully discrete finite element scheme, obtaining optimal first order approximation for velocity and pressure with respect to the max-norm in time and the H-1 x L-2-norm in space. The proof of these error estimates are based on three main points: a) provide some new estimates for the time-discrete scheme (not proved in [15]) which must be now used, b) give a discrete version of the H-2 x H-1 estimates in FE spaces, using stability in the W-1,W-6 x L-6-norm of the FE Stokes projector, and c) the use of a weight function vanishing at initial time will let to hold the error estimates without imposing global compatibility for the exact solution.
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页码:826 / 844
页数:19
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