This paper is devoted to the establishment of sharper a priori stability and error estimates of a stabilized finite element method proposed by Barrenechea and Valentin for solving the generalized Stokes problem,which ...This paper is devoted to the establishment of sharper a priori stability and error estimates of a stabilized finite element method proposed by Barrenechea and Valentin for solving the generalized Stokes problem,which involves a viscosity v and a reaction consta nt a.With the establishmen t of sharper st ability estimates and the help of ad hoc finite element projections,we can explicitly establish the dependence of error bounds of velocity and pressure on the viscosity z/,the reaction constant cr,and the mesh size h.Our analysis reveals that the viscosity y and the reaction constant a respectively act in the numerator position and the denominator position in the error estimates of velocity and pressure in standard norms without any weights.Consequently,the stabilization method is indeed suitable for the generalized Stokes problem with a small viscosity u and a large reaction constant a.The sharper error estimates agree very well with the numerical results.展开更多
基金The work of H.Y.Duan was supported by the National Natural Science Foundation of China under grants 11971366,11571266,11661161017,1117116&11071132the Collaborative Innovation Centre of Mat hematics,and the Hubei Key Laboratory of Computational Science(Wuhan University,the Natural Science Foundation of Hubei Province No.2019CFA007).
文摘This paper is devoted to the establishment of sharper a priori stability and error estimates of a stabilized finite element method proposed by Barrenechea and Valentin for solving the generalized Stokes problem,which involves a viscosity v and a reaction consta nt a.With the establishmen t of sharper st ability estimates and the help of ad hoc finite element projections,we can explicitly establish the dependence of error bounds of velocity and pressure on the viscosity z/,the reaction constant cr,and the mesh size h.Our analysis reveals that the viscosity y and the reaction constant a respectively act in the numerator position and the denominator position in the error estimates of velocity and pressure in standard norms without any weights.Consequently,the stabilization method is indeed suitable for the generalized Stokes problem with a small viscosity u and a large reaction constant a.The sharper error estimates agree very well with the numerical results.
