A family of conforming finite elements are designed on rectangular grids for solving the Reissner-Mindlin plate equation.The rotation is approximated by C^(1)-Q_(k+1)in one direction and C^(0)-Q_(k)in the other direct...A family of conforming finite elements are designed on rectangular grids for solving the Reissner-Mindlin plate equation.The rotation is approximated by C^(1)-Q_(k+1)in one direction and C^(0)-Q_(k)in the other direction finite elements.The displacement is approximated by C^(1)-Q_(k+1,k+1).The method is locking-free without using any projection/reduction operator.Theoretical proof and numerical confirmation are presented.展开更多
A novel conforming discontinuous Galerkin(CDG)finite element method is introduced for the Poisson equation on rectangular meshes.This CDG method with discontinuous P_(k)(k≥1)elements converges to the true solution tw...A novel conforming discontinuous Galerkin(CDG)finite element method is introduced for the Poisson equation on rectangular meshes.This CDG method with discontinuous P_(k)(k≥1)elements converges to the true solution two orders above the continuous finite element counterpart.Superconvergence of order two for the CDG finite element solution is proved in an energy norm and the L^(2)norm.A local post-process is defined which lifts a P_(k)CDG solution to a discontinuous P_(k+2)solution.It is proved that the lifted P_(k+2)solution converges at the optimal order.The numerical tests illustrate the theoretic findings.展开更多
This paper is to study the convergence and superconvergence of rectangular finite elements under anisotropic meshes. By using of the orthogonal expansion method, an anisotropic Lagrange interpolation is presented. The...This paper is to study the convergence and superconvergence of rectangular finite elements under anisotropic meshes. By using of the orthogonal expansion method, an anisotropic Lagrange interpolation is presented. The family of Lagrange rectangular elements with all the possible shape function spaces are considered, which cover the Intermediate families, Tensor-product families and Serendipity families. It is shown that the anisotropic interpolation error estimates hold for any order Sobolev norm. We extend the convergence and superconvergence result of rectangular finite elements to arbitrary rectangular meshes in a unified way.展开更多
In this paper,several new energy identities of metamaterial Maxwell’s equations with the perfectly electric conducting(PEC)boundary condition are proposed and proved.These new energy identities are different from the...In this paper,several new energy identities of metamaterial Maxwell’s equations with the perfectly electric conducting(PEC)boundary condition are proposed and proved.These new energy identities are different from the Poynting theorem.By using these new energy identities,it is proved that the Yee scheme on non-uniform rectangular meshes is stable in the discrete L2 and H1 norms when the Courant-Friedrichs-Lewy(CFL)condition is satisfied.Numerical experiments in twodimension(2D)and 3D are carried out and confirm our analysis,and the superconvergence in the discrete H1 norm is found.展开更多
A quasi-rectangular mesh (denoted by △QR) is basically a rectangular mesh (△R) that allows local modifications, including T-mesh (△T) and L-mesh (△L). In this paper, the dimensions of the bivariate spline spaces S...A quasi-rectangular mesh (denoted by △QR) is basically a rectangular mesh (△R) that allows local modifications, including T-mesh (△T) and L-mesh (△L). In this paper, the dimensions of the bivariate spline spaces Skμ(△QR) are discussed by using the Smoothing Cofactor-Conformality method. The dimension formulae are obtained with some constraints depending on the order of the smoothness, the degree of the spline functions and the structure of the mesh as well.展开更多
文摘A family of conforming finite elements are designed on rectangular grids for solving the Reissner-Mindlin plate equation.The rotation is approximated by C^(1)-Q_(k+1)in one direction and C^(0)-Q_(k)in the other direction finite elements.The displacement is approximated by C^(1)-Q_(k+1,k+1).The method is locking-free without using any projection/reduction operator.Theoretical proof and numerical confirmation are presented.
文摘A novel conforming discontinuous Galerkin(CDG)finite element method is introduced for the Poisson equation on rectangular meshes.This CDG method with discontinuous P_(k)(k≥1)elements converges to the true solution two orders above the continuous finite element counterpart.Superconvergence of order two for the CDG finite element solution is proved in an energy norm and the L^(2)norm.A local post-process is defined which lifts a P_(k)CDG solution to a discontinuous P_(k+2)solution.It is proved that the lifted P_(k+2)solution converges at the optimal order.The numerical tests illustrate the theoretic findings.
文摘This paper is to study the convergence and superconvergence of rectangular finite elements under anisotropic meshes. By using of the orthogonal expansion method, an anisotropic Lagrange interpolation is presented. The family of Lagrange rectangular elements with all the possible shape function spaces are considered, which cover the Intermediate families, Tensor-product families and Serendipity families. It is shown that the anisotropic interpolation error estimates hold for any order Sobolev norm. We extend the convergence and superconvergence result of rectangular finite elements to arbitrary rectangular meshes in a unified way.
基金supported by the National Natural Science Foundation of China Grant No.11671233 and the Shandong Provincial Science and Technology Development Program Grant No.2018GGX101036.
文摘In this paper,several new energy identities of metamaterial Maxwell’s equations with the perfectly electric conducting(PEC)boundary condition are proposed and proved.These new energy identities are different from the Poynting theorem.By using these new energy identities,it is proved that the Yee scheme on non-uniform rectangular meshes is stable in the discrete L2 and H1 norms when the Courant-Friedrichs-Lewy(CFL)condition is satisfied.Numerical experiments in twodimension(2D)and 3D are carried out and confirm our analysis,and the superconvergence in the discrete H1 norm is found.
基金the National Natural Science Foundation of China (Nos.60533060 10726067)+1 种基金the Natural Science Foundation for Doctoral Career of Liaoning Province (No.20061060)the Science Foundation of Dalian University of Technology (No.SFDUT07001)
文摘A quasi-rectangular mesh (denoted by △QR) is basically a rectangular mesh (△R) that allows local modifications, including T-mesh (△T) and L-mesh (△L). In this paper, the dimensions of the bivariate spline spaces Skμ(△QR) are discussed by using the Smoothing Cofactor-Conformality method. The dimension formulae are obtained with some constraints depending on the order of the smoothness, the degree of the spline functions and the structure of the mesh as well.
