Regular assumption of finite element meshes is a basic condition of most analysis of finite element approximations both for conventional conforming elements and nonconforming elements. The aim of this paper is to pres...Regular assumption of finite element meshes is a basic condition of most analysis of finite element approximations both for conventional conforming elements and nonconforming elements. The aim of this paper is to present a novel approach of dealing with the approximation of a four-degree nonconforming finite element for the second order elliptic problems on the anisotropic meshes. The optimal error estimates of energy norm and L^2-norm without the regular assumption or quasi-uniform assumption are obtained based on some new special features of this element discovered herein. Numerical results are given to demonstrate validity of our theoretical analysis.展开更多
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
A nonconforming H^1-Calerkin mixed finite element method is analyzed for Sobolev equations on anisotropic meshes. The error estimates are obtained without using Ritz-Volterra projection.
Quasi-Wilson nonconforming finite element approximation for a class of nonlinear Sobolev equa- tions is discussed on rectangular meshes. We first prove that this element has two special characters by novel approaches....Quasi-Wilson nonconforming finite element approximation for a class of nonlinear Sobolev equa- tions is discussed on rectangular meshes. We first prove that this element has two special characters by novel approaches. One is that （Vh（U -- Ihu）,VhVh）h may be estimated as order O（h2） when u E H3（Ω）, where Iuu denotes the bilinear interpolation of u, vh is a polynomial belongs to quasi-Wilson finite element space and △h denotes the piecewise defined gradient operator, h is the mesh size tending to zero. The other is that the consistency error of this element is of order O（h2）/O（h3） in broken Hi-norm, which is one/two order higher than its interpolation error when u ε Ha（Ω）/H4 （（1）. Then we derive the optimal order error estimate and su- perclose property via mean-value method and the known high accuracy result of bilinear element. Furthermore, we deduce the global superconvergence through interpolation post processing technique. At last, an extrapola- tion result of order O（h3）, two order higher than traditional error estimate, is obtained by constructing a new suitable extrapolation scheme.展开更多
The main aim of this paper is to study the superconvergence accuracy analysis of the famous ACM＇s nonconforming finite element for biharmonic equation under anisotropic meshes. By using some novel approaches and tech...The main aim of this paper is to study the superconvergence accuracy analysis of the famous ACM＇s nonconforming finite element for biharmonic equation under anisotropic meshes. By using some novel approaches and techniques, the optimal anisotropic interpolation error and consistency error estimates are obtained. The global error is of order O（h^2）. Lastly, some numerical tests are presented to verify the theoretical analysis.展开更多
In this paper, a new splitting positive definite nonconforming mixed finite element method is proposed for pseudo-hyperbolic equations, in which a quasi-Wilson quadrilateral element is used for the flux p, and the bil...In this paper, a new splitting positive definite nonconforming mixed finite element method is proposed for pseudo-hyperbolic equations, in which a quasi-Wilson quadrilateral element is used for the flux p, and the bilinear element is used for u. Superconvergence results in ｜｜·｜｜div,h norm for p and optimal error estimates in L2 norm for u are derived for both semi-discrete and fully discrete schemes under almost uniform meshes.展开更多
EQrot nonconforming finite element approximation to a class of nonlinear dual phase lagging heat conduction equations is discussed for semi-discrete and fully-discrete schemes. By use of a special property, that is, t...EQrot nonconforming finite element approximation to a class of nonlinear dual phase lagging heat conduction equations is discussed for semi-discrete and fully-discrete schemes. By use of a special property, that is, the consistency error of this element is of order O（h2） one order higher than its interpolation error O（h）, the superclose results of order O（h2） in broken Hi-norm are obtained. At the same time, the global superconvergence in broken Hi-norm is deduced by interpolation postprocessing technique. Moreover, the extrapolation result with order O（h4） is derived by constructing a new interpolation postprocessing operator and extrapolation scheme based on the known asymptotic expansion formulas of EQrot element. Finally, optimal error estimate is gained for a proposed fully-discrete scheme by different approaches from the previous literature.展开更多
文摘Regular assumption of finite element meshes is a basic condition of most analysis of finite element approximations both for conventional conforming elements and nonconforming elements. The aim of this paper is to present a novel approach of dealing with the approximation of a four-degree nonconforming finite element for the second order elliptic problems on the anisotropic meshes. The optimal error estimates of energy norm and L^2-norm without the regular assumption or quasi-uniform assumption are obtained based on some new special features of this element discovered herein. Numerical results are given to demonstrate validity of our theoretical analysis.
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.
基金Supported by the National Natural Science Foundation of China(No.10671184).
文摘A nonconforming H^1-Calerkin mixed finite element method is analyzed for Sobolev equations on anisotropic meshes. The error estimates are obtained without using Ritz-Volterra projection.
基金Supported by National Natural Science Foundation of China (Grant Nos. 10971203 11101381+4 种基金 11271340)Specialized Research Fund for the Doctoral Program of Higher Education (Grant No. 20094101110006)Tianyuan Mathematics Foundation of the National Natural Science Foundation of China(Grant No. 11026154)the Natural Science Foundation of Henan Province (Grant Nos. 112300410026 122300410266)
文摘Quasi-Wilson nonconforming finite element approximation for a class of nonlinear Sobolev equa- tions is discussed on rectangular meshes. We first prove that this element has two special characters by novel approaches. One is that （Vh（U -- Ihu）,VhVh）h may be estimated as order O（h2） when u E H3（Ω）, where Iuu denotes the bilinear interpolation of u, vh is a polynomial belongs to quasi-Wilson finite element space and △h denotes the piecewise defined gradient operator, h is the mesh size tending to zero. The other is that the consistency error of this element is of order O（h2）/O（h3） in broken Hi-norm, which is one/two order higher than its interpolation error when u ε Ha（Ω）/H4 （（1）. Then we derive the optimal order error estimate and su- perclose property via mean-value method and the known high accuracy result of bilinear element. Furthermore, we deduce the global superconvergence through interpolation post processing technique. At last, an extrapola- tion result of order O（h3）, two order higher than traditional error estimate, is obtained by constructing a new suitable extrapolation scheme.
文摘The main aim of this paper is to study the superconvergence accuracy analysis of the famous ACM＇s nonconforming finite element for biharmonic equation under anisotropic meshes. By using some novel approaches and techniques, the optimal anisotropic interpolation error and consistency error estimates are obtained. The global error is of order O（h^2）. Lastly, some numerical tests are presented to verify the theoretical analysis.
基金Supported by the National Natural Science Foundation of China(No.10971203,11271340,11101384)the Specialized Research Fund for the Doctoral Program of Higher Education(No.20094101110006)
文摘In this paper, a new splitting positive definite nonconforming mixed finite element method is proposed for pseudo-hyperbolic equations, in which a quasi-Wilson quadrilateral element is used for the flux p, and the bilinear element is used for u. Superconvergence results in ｜｜·｜｜div,h norm for p and optimal error estimates in L2 norm for u are derived for both semi-discrete and fully discrete schemes under almost uniform meshes.
基金Supported by the National Natural Science Foundation of China (Nos. 10971203 11101381)+3 种基金Tianyuan Mathe-matics Foundation of National Natural Science Foundation of China (No. 11026154)Natural Science Foundation of Henan Province (No. 112300410026)Natural Science Foundation of the Education Department of Henan Province (Nos. 2011A110020 12A110021)
文摘EQrot nonconforming finite element approximation to a class of nonlinear dual phase lagging heat conduction equations is discussed for semi-discrete and fully-discrete schemes. By use of a special property, that is, the consistency error of this element is of order O（h2） one order higher than its interpolation error O（h）, the superclose results of order O（h2） in broken Hi-norm are obtained. At the same time, the global superconvergence in broken Hi-norm is deduced by interpolation postprocessing technique. Moreover, the extrapolation result with order O（h4） is derived by constructing a new interpolation postprocessing operator and extrapolation scheme based on the known asymptotic expansion formulas of EQrot element. Finally, optimal error estimate is gained for a proposed fully-discrete scheme by different approaches from the previous literature.
