An H^1-Galerkin mixed finite element method is discussed for a class of second order SchrSdinger equation. Optimal error estimates of semidiscrete schemes are derived for problems in one space dimension. At the same t...An H^1-Galerkin mixed finite element method is discussed for a class of second order SchrSdinger equation. Optimal error estimates of semidiscrete schemes are derived for problems in one space dimension. At the same time, optimal error estimates are derived for fully discrete schemes. And it is showed that the H1-Galerkin mixed finite element approximations have the same rate of convergence as in the classical mixed finite element methods without requiring the LBB consistency condition.展开更多
The main aim of this article is to study the approximation of a locking-free anisotropic nonconforming finite element for the pure displacement boundary value problem of planar linear elasticity. The optimal error est...The main aim of this article is to study the approximation of a locking-free anisotropic nonconforming finite element for the pure displacement boundary value problem of planar linear elasticity. The optimal error estimates are obtained by using some novel approaches and techniques. The method proposed in this article is robust in the sense that the convergence estimates in the energy and L^2-norms are independent-of the Lame parameter λ.展开更多
In this paper, we propose an Expanded Characteristic-mixed Finite Element Method for approximating the solution to a convection dominated transport problem. The method is a combination of characteristic approximation ...In this paper, we propose an Expanded Characteristic-mixed Finite Element Method for approximating the solution to a convection dominated transport problem. The method is a combination of characteristic approximation to handle the convection part in time and an expanded mixed finite element spatial approximation to deal with the diffusion part. The scheme is stable since fluid is transported along the approximate characteristics on the discrete level. At the same time it expands the standard mixed finite element method in the sense that three variables are explicitly treated： the scalar unknown, its gradient, and its flux. Our analysis shows the method approximates the scalar unknown, its gradient, and its flux optimally and simultaneously. We also show this scheme has much smaller time-truncation errors than those of standard methods. A numerical example is presented to show that the scheme is of high performance.展开更多
In this paper, we study numerical approximations of a recently proposed phase field model for the vesicle membrane deformation governed by the variation of the elastic bending energy. To overcome the challenges of hig...In this paper, we study numerical approximations of a recently proposed phase field model for the vesicle membrane deformation governed by the variation of the elastic bending energy. To overcome the challenges of high order nonlinear differential systems and the nonlinear constraints associated with the problem, we present the phase field bending elasticity model in a nested saddle point formulation. A mixed finite element method is then employed to compute the equilibrium configuration of a vesicle membrane with prescribed volume and surface area. Coupling the approximation results for a related linearized problem and the general theory of Brezzi-Rappaz-Raviart, optimal order error estimates for the finite element approximations of the phase field model are obtained. Numerical results are provided to substantiate the derived estimates.展开更多
In this paper, we discuss the quadrilateral, finite element approximation to the two-dimensional linear elasticity problem associated with a homogeneous isotropic elastic material. The optimal convergence of the finit...In this paper, we discuss the quadrilateral, finite element approximation to the two-dimensional linear elasticity problem associated with a homogeneous isotropic elastic material. The optimal convergence of the finite element method is proved for both the L-2-norm and energy-norm, and in particular, the convergence is uniform with respect to the Lame constant lambda. Also the performance of the scheme does not deteriorate as the material becomes nearly incompressible, Numerical experiments are given which are consistent with our theory.展开更多
基金Supported by the National Natural Science Foundation of China (10601022)Natural Science Foundation of Inner Mongolia Autonomous Region (200607010106)Youth Science Foundation of Inner Mongolia University(ND0702)
文摘An H^1-Galerkin mixed finite element method is discussed for a class of second order SchrSdinger equation. Optimal error estimates of semidiscrete schemes are derived for problems in one space dimension. At the same time, optimal error estimates are derived for fully discrete schemes. And it is showed that the H1-Galerkin mixed finite element approximations have the same rate of convergence as in the classical mixed finite element methods without requiring the LBB consistency condition.
基金The research is supported by NSF of China (10371113 10471133)
文摘The main aim of this article is to study the approximation of a locking-free anisotropic nonconforming finite element for the pure displacement boundary value problem of planar linear elasticity. The optimal error estimates are obtained by using some novel approaches and techniques. The method proposed in this article is robust in the sense that the convergence estimates in the energy and L^2-norms are independent-of the Lame parameter λ.
基金This work is supported by the Natural Science Foundation of China （Grant No.10271068）, the Natural Science Foundation of Shandong Province （No.Y2002A01）, China, and the Science Foundation For Young Scientist in Shandong Province （No.2004BS01009）.
文摘In this paper, we propose an Expanded Characteristic-mixed Finite Element Method for approximating the solution to a convection dominated transport problem. The method is a combination of characteristic approximation to handle the convection part in time and an expanded mixed finite element spatial approximation to deal with the diffusion part. The scheme is stable since fluid is transported along the approximate characteristics on the discrete level. At the same time it expands the standard mixed finite element method in the sense that three variables are explicitly treated： the scalar unknown, its gradient, and its flux. Our analysis shows the method approximates the scalar unknown, its gradient, and its flux optimally and simultaneously. We also show this scheme has much smaller time-truncation errors than those of standard methods. A numerical example is presented to show that the scheme is of high performance.
文摘In this paper, we study numerical approximations of a recently proposed phase field model for the vesicle membrane deformation governed by the variation of the elastic bending energy. To overcome the challenges of high order nonlinear differential systems and the nonlinear constraints associated with the problem, we present the phase field bending elasticity model in a nested saddle point formulation. A mixed finite element method is then employed to compute the equilibrium configuration of a vesicle membrane with prescribed volume and surface area. Coupling the approximation results for a related linearized problem and the general theory of Brezzi-Rappaz-Raviart, optimal order error estimates for the finite element approximations of the phase field model are obtained. Numerical results are provided to substantiate the derived estimates.
文摘In this paper, we discuss the quadrilateral, finite element approximation to the two-dimensional linear elasticity problem associated with a homogeneous isotropic elastic material. The optimal convergence of the finite element method is proved for both the L-2-norm and energy-norm, and in particular, the convergence is uniform with respect to the Lame constant lambda. Also the performance of the scheme does not deteriorate as the material becomes nearly incompressible, Numerical experiments are given which are consistent with our theory.
