This paper is devoted to the five parameters nonconforming finite element schemes with moving grids for velocity-pressure mixed formulations of the nonstationary Stokes problem in 2-D. We show that this element has an...This paper is devoted to the five parameters nonconforming finite element schemes with moving grids for velocity-pressure mixed formulations of the nonstationary Stokes problem in 2-D. We show that this element has anisotropic behavior and derive anisotropic error estimations in some certain norms of the velocity and the pressure based on some novel techniques. Especially through careful analysis we get an interesting result on consistency error estimation, which has never been seen for mixed finite element methods in the previously literatures.展开更多
The purpose of this paper is to investigate the convergence of the mixed finite element method for the initial-boundary value problem for the Sobolev equation Ut-div{aut + b1 u} = f based on the Raviart-Thomas space ...The purpose of this paper is to investigate the convergence of the mixed finite element method for the initial-boundary value problem for the Sobolev equation Ut-div{aut + b1 u} = f based on the Raviart-Thomas space Vh × Wh H(div; × L2(). Optimal order estimates are obtained for the approximation of u, ut, the associated velocity p and divp respectively in L(0,T;L2()), L(0,T;L2()), L(0,T;L2()2), and L2(0, T; L2()). Quasi-optimal order estimates are obtained for the approximations of u, ut in L(0, T; L()) and p in L(0,T; L()2).展开更多
Abstract In this paper, we apply EQ1^rot nonconforming finite element to approximate Signorini problem. If 5 the exact solution u EQ1^rot, the error estimate of order O（h） about the broken energy norm is obtained f...Abstract In this paper, we apply EQ1^rot nonconforming finite element to approximate Signorini problem. If 5 the exact solution u EQ1^rot, the error estimate of order O（h） about the broken energy norm is obtained for quadrilateral meshes satisfying regularity assumption and bi-section condition. Furthermore, the superconver- gence results of order EQ1^rot are derived for rectangular meshes. Numerical results are presented to confirm the considered theory.展开更多
In this paper, we discuss a posteriori error estimates of the eigenvalue λ[sub h] given by Adini nonconforming finite element. We give an assymptotically exact error estimator of the λ[sub h]. We prove that the orde...In this paper, we discuss a posteriori error estimates of the eigenvalue λ[sub h] given by Adini nonconforming finite element. We give an assymptotically exact error estimator of the λ[sub h]. We prove that the order of convergence of the λ[sub h] is just 2 and the converge from below for sufficiently small h. [ABSTRACT FROM AUTHOR]展开更多
基金This research is supported by the National Science Foundation of China（No.10371113）.The authors would like to thank the anonymous referees for their helpful suggestions.
文摘This paper is devoted to the five parameters nonconforming finite element schemes with moving grids for velocity-pressure mixed formulations of the nonstationary Stokes problem in 2-D. We show that this element has anisotropic behavior and derive anisotropic error estimations in some certain norms of the velocity and the pressure based on some novel techniques. Especially through careful analysis we get an interesting result on consistency error estimation, which has never been seen for mixed finite element methods in the previously literatures.
文摘The purpose of this paper is to investigate the convergence of the mixed finite element method for the initial-boundary value problem for the Sobolev equation Ut-div{aut + b1 u} = f based on the Raviart-Thomas space Vh × Wh H(div; × L2(). Optimal order estimates are obtained for the approximation of u, ut, the associated velocity p and divp respectively in L(0,T;L2()), L(0,T;L2()), L(0,T;L2()2), and L2(0, T; L2()). Quasi-optimal order estimates are obtained for the approximations of u, ut in L(0, T; L()) and p in L(0,T; L()2).
基金supported by National Natural Science Foundation of China (Grant Nos.10971203 and 11271340)Research Fund for the Doctoral Program of Higher Education of China (Grant No.20094101110006)
文摘Abstract In this paper, we apply EQ1^rot nonconforming finite element to approximate Signorini problem. If 5 the exact solution u EQ1^rot, the error estimate of order O（h） about the broken energy norm is obtained for quadrilateral meshes satisfying regularity assumption and bi-section condition. Furthermore, the superconver- gence results of order EQ1^rot are derived for rectangular meshes. Numerical results are presented to confirm the considered theory.
文摘In this paper, we discuss a posteriori error estimates of the eigenvalue λ[sub h] given by Adini nonconforming finite element. We give an assymptotically exact error estimator of the λ[sub h]. We prove that the order of convergence of the λ[sub h] is just 2 and the converge from below for sufficiently small h. [ABSTRACT FROM AUTHOR]
