In this paper, it is shown that Quasi-Wilson clement possesses a very special property i.e. the consistency error is of order O(h(2)), one order higher than that of Wilson element.
The Wilson finite element method is considered to solve a class of two- dimensional second order elliptic boundary value problems. By using of the particular structure of the element and some new techniques, we obtain...The Wilson finite element method is considered to solve a class of two- dimensional second order elliptic boundary value problems. By using of the particular structure of the element and some new techniques, we obtain the superclose and global superconvergence on anisotropic meshes. Numerical example is also given to confirm our theoretical analysis.展开更多
In this paper the equivalence of the generalized hybrid element and the modified Wilson element, which is derived by the generalized hybrid method, is proved.
In this paper, a new higher order Wilson element is presented, and the convergence is proved. Then the interpolation postprocessing technique is used to obtain the global superconvergence and posterior error estimate ...In this paper, a new higher order Wilson element is presented, and the convergence is proved. Then the interpolation postprocessing technique is used to obtain the global superconvergence and posterior error estimate of higher accuracy of this new element for the Sobolev type equations.展开更多
In this paper, the Wilson nonconforming finite element is considered for solving a class of second-order elliptic boundary value problems. Based on an asymptotic error expansion for the Wilson finite element, the glob...In this paper, the Wilson nonconforming finite element is considered for solving a class of second-order elliptic boundary value problems. Based on an asymptotic error expansion for the Wilson finite element, the global superconvergences, the local superconvergences and the defect correction schemes are presented.展开更多
This paper discusses the optimal preconditioning in the domain decomposition method for Wilson element. The process of the preconditioning is composed of the resolution of a small scale global problem based on a coars...This paper discusses the optimal preconditioning in the domain decomposition method for Wilson element. The process of the preconditioning is composed of the resolution of a small scale global problem based on a coarser grid and a number of independent local subproblems, which can be chosen arbitrarily. The condition number of the preconditioned system is estimated by some characteristic numbers related to global and local subproblems. With a proper selection, the optimal preconditioner can be obtained, while the condition number is independent of the scale of the problem and the number of subproblems.展开更多
In this paper,we analyze the Wilson element method of the eigenvalue problem in arbitrary dimensions by combining a new technique recently developed in[10]and the a posteriori error result.We prove that the discrete e...In this paper,we analyze the Wilson element method of the eigenvalue problem in arbitrary dimensions by combining a new technique recently developed in[10]and the a posteriori error result.We prove that the discrete eigenvalues are smaller than the exact ones.展开更多
In this paper the Wilson nonconforming finite element is employed to solve Sobolev and viscoelasticity type equations. By means of post-processing technique, global superconvergence estimates are obtained for quasi-un...In this paper the Wilson nonconforming finite element is employed to solve Sobolev and viscoelasticity type equations. By means of post-processing technique, global superconvergence estimates are obtained for quasi-uniform rectangular meshes. Finally, an error correction scheme is presented.展开更多
In this article, we study the explicit expressions of the constants in the error estimate of the nonconforming finite element method. We explicitly obtain the approximation error estimate and the consistency error est...In this article, we study the explicit expressions of the constants in the error estimate of the nonconforming finite element method. We explicitly obtain the approximation error estimate and the consistency error estimate for the Wilson＇s element without the regular assumption, respectively, which implies the final finite element error estimate. Such explicit a priori error estimates can be used as computable error bounds.展开更多
Cascadic multigrid technique for mortar Wilson finite element method ofhomogeneous boundary value planar linear elasticity is described and analyzed. Firstthe mortar Wilson finite element method for planar linear elas...Cascadic multigrid technique for mortar Wilson finite element method ofhomogeneous boundary value planar linear elasticity is described and analyzed. Firstthe mortar Wilson finite element method for planar linear elasticity will be analyzed,and the error estimate under L2 and H1 norm is optimal. Then a cascadic multigridmethod for the mortar finite element discrete problem is described. Suitable grid trans-fer operator and smoother are developed which lead to an optimal cascadic multigridmethod. Finally, the computational results are presented.展开更多
文摘In this paper, it is shown that Quasi-Wilson clement possesses a very special property i.e. the consistency error is of order O(h(2)), one order higher than that of Wilson element.
基金Project supported by the National Natural Science Foundation of China (No. 10371113)
文摘The Wilson finite element method is considered to solve a class of two- dimensional second order elliptic boundary value problems. By using of the particular structure of the element and some new techniques, we obtain the superclose and global superconvergence on anisotropic meshes. Numerical example is also given to confirm our theoretical analysis.
基金The project is supported by the National Natural Science Foundation of China
文摘In this paper the equivalence of the generalized hybrid element and the modified Wilson element, which is derived by the generalized hybrid method, is proved.
基金the National Natural Science Foundation of China(10671184)
文摘In this paper, a new higher order Wilson element is presented, and the convergence is proved. Then the interpolation postprocessing technique is used to obtain the global superconvergence and posterior error estimate of higher accuracy of this new element for the Sobolev type equations.
文摘In this paper, the Wilson nonconforming finite element is considered for solving a class of second-order elliptic boundary value problems. Based on an asymptotic error expansion for the Wilson finite element, the global superconvergences, the local superconvergences and the defect correction schemes are presented.
文摘This paper discusses the optimal preconditioning in the domain decomposition method for Wilson element. The process of the preconditioning is composed of the resolution of a small scale global problem based on a coarser grid and a number of independent local subproblems, which can be chosen arbitrarily. The condition number of the preconditioned system is estimated by some characteristic numbers related to global and local subproblems. With a proper selection, the optimal preconditioner can be obtained, while the condition number is independent of the scale of the problem and the number of subproblems.
基金The work is supported by the PHR(IHLB)project under Grant PHR20110874the NSFC project under Grant 11101013the PHR(IHLB)project under Grant PHR201102.
文摘In this paper,we analyze the Wilson element method of the eigenvalue problem in arbitrary dimensions by combining a new technique recently developed in[10]and the a posteriori error result.We prove that the discrete eigenvalues are smaller than the exact ones.
文摘In this paper the Wilson nonconforming finite element is employed to solve Sobolev and viscoelasticity type equations. By means of post-processing technique, global superconvergence estimates are obtained for quasi-uniform rectangular meshes. Finally, an error correction scheme is presented.
基金supported by National Natural Science Foundation of China (11071226 11201122)
文摘In this article, we study the explicit expressions of the constants in the error estimate of the nonconforming finite element method. We explicitly obtain the approximation error estimate and the consistency error estimate for the Wilson＇s element without the regular assumption, respectively, which implies the final finite element error estimate. Such explicit a priori error estimates can be used as computable error bounds.
基金The project is supported by the Special Funds for Major State Basic Research Projects G19990328 and the National Natural Science Foundation of China(No.10071015)
文摘Cascadic multigrid technique for mortar Wilson finite element method ofhomogeneous boundary value planar linear elasticity is described and analyzed. Firstthe mortar Wilson finite element method for planar linear elasticity will be analyzed,and the error estimate under L2 and H1 norm is optimal. Then a cascadic multigridmethod for the mortar finite element discrete problem is described. Suitable grid trans-fer operator and smoother are developed which lead to an optimal cascadic multigridmethod. Finally, the computational results are presented.
