Isoparametric quadrilateral elements are widely used in the finite element method, but the accuracy of the isoparametric quadrilateral elements will drop obviously deteriorate due to mesh distortions. Spline functions...Isoparametric quadrilateral elements are widely used in the finite element method, but the accuracy of the isoparametric quadrilateral elements will drop obviously deteriorate due to mesh distortions. Spline functions have some properties of simplicity and conformality. Two 8-node quadrilateral elements have been developed using the trian- gular area coordinates and the B-net method, which can ex- actly model the quadratic field for both convex and concave quadrangles. Some appropriate examples are employed to evaluate the performance of the proposed elements. The nu- merical results show that the two spline elements can obtain solutions which are highly accurate and insensitive to mesh distortions.展开更多
C^1 natural element method （C^1 NEM） is applied to strain gradient linear elasticity, and size effects on mi crostructures are analyzed. The shape functions in C^1 NEM are built upon the natural neighbor interpolati...C^1 natural element method （C^1 NEM） is applied to strain gradient linear elasticity, and size effects on mi crostructures are analyzed. The shape functions in C^1 NEM are built upon the natural neighbor interpolation （NNI）, with interpolation realized to nodal function and nodal gradient values, so that the essential boundary conditions （EBCs） can be imposed directly in a Galerkin scheme for partial differential equations （PDEs）. In the present paper, C^1 NEM for strain gradient linear elasticity is constructed, and sev- eral typical examples which have analytical solutions are presented to illustrate the effectiveness of the constructed method. In its application to microstructures, the size effects of bending stiffness and stress concentration factor （SCF） are studied for microspeciem and microgripper, respectively. It is observed that the size effects become rather strong when the width of spring for microgripper, the radius of circular perforation and the long axis of elliptical perforation for microspeciem come close to the material characteristic length scales. For the U-shaped notch, the size effects decline obviously with increasing notch radius, and decline mildly with increasing length of notch.展开更多
This article will combine the finite element method, the interpolated coefficient finite element method, the eigenfunction expansion method, and the search-extension method to obtain the multiple solutions for semilin...This article will combine the finite element method, the interpolated coefficient finite element method, the eigenfunction expansion method, and the search-extension method to obtain the multiple solutions for semilinear elliptic equations. This strategy not only grently reduces the expensive computation, but also is successfully implemented to obtain multiple solutions for a class of semilinear elliptic boundary value problems with non-odd nonlinearity on some convex or nonconvex domains. Numerical solutions illustrated by their graphics for visualization will show the efficiency of the approach.展开更多
We assessed the contamination levels of Mn, Zn, Cr, Cu, Ni, Pb, As and Hg and the risks posed by these potentially harmful elements in top-soils around a municipal solid waste incinerator （MSWI）. We collected 20 soi...We assessed the contamination levels of Mn, Zn, Cr, Cu, Ni, Pb, As and Hg and the risks posed by these potentially harmful elements in top-soils around a municipal solid waste incinerator （MSWI）. We collected 20 soil samples, with an average pH of 8.1, and another fly ash sample emitted from the MSWI to investigate the concentrations of these elements in soils. We determined the concentrations of these elements by inductively coupled plasma-optical emission spectrometer （ICP-OES）, except for Hg, which we measured by AF-610B atomic fluorescence spectrometer （AFS）. We assessed the risks of these elements through the use of geoaccumulation index （/geo）, potential ecological risk index （R/）, hazard quotient （HQi） and cancer risk （Riski）. The results showed that concentrations of potentially harmful elements in soil were influenced by the wind direction, and the concentrations of most elements were higher in the area northwest of the MSWI, compared with the area southeast of the incinerator, with the exception of As; these results were in accordance with those results acquired from our contour maps. According to the I^o values, some soil samples were clearly polluted by Hg emissions. However, the health risk assessment indicated that the concentrations of Hg and other elements in soil did not pose non-carcinogenic risks to the local populations. This was also the case for the carcinogenic risks posed by As Cr and Ni. The carcinogenic risk posed by As was higher in the range 6.49 × 10 -9.58 × 10 -6, but this was still considered to be an acceptable level of risk.展开更多
In this paper we extend the idea of interpolated coefficients for a semilinear problem to the quadratic triangular finite volume element method.At first we introduce quadratic triangular finite volume element method w...In this paper we extend the idea of interpolated coefficients for a semilinear problem to the quadratic triangular finite volume element method.At first we introduce quadratic triangular finite volume element method with interpolated coefficients for a boundary value problem of semilinear elliptic equation.Next we derive convergence estimate in H1-norm,L2-norm and L¥-norm,respectively.Finally an example is given to illustrate the effectiveness of the proposed method.展开更多
The aim of this paper is to lay a algebraic geometry foundation for constructing smoothing interpolants on curved side element. Some interpolation theorems in polynomial space are given. The main results effectively f...The aim of this paper is to lay a algebraic geometry foundation for constructing smoothing interpolants on curved side element. Some interpolation theorems in polynomial space are given. The main results effectively for CAGD are presented.展开更多
In this paper we extend the idea of interpolated coefficients for a semilinear problem to the triangular finite volume element method. We first introduce triangular finite volume element method with interpolated coeff...In this paper we extend the idea of interpolated coefficients for a semilinear problem to the triangular finite volume element method. We first introduce triangular finite volume element method with interpolated coefficients for a boundary value problem of semilinear elliptic equation. We then derive convergence estimate in Hi-norm, L2-norm and L∞-norm, respectively. Finally an example is given to illustrate the effectiveness of the proposed method.展开更多
The aim of this paper is to provide a local superconvergence analysis for ined finite element methods of Poission equation. We shall prove that if p is smmoth enough in a local regionΩ0Ω1Ω and rectangular mesh is ...The aim of this paper is to provide a local superconvergence analysis for ined finite element methods of Poission equation. We shall prove that if p is smmoth enough in a local regionΩ0Ω1Ω and rectangular mesh is imposed onΩ1, then local superconvergence for are expected. Thus, by post-processing operators P and we have obtained the follwing local superconvergence error estimate:展开更多
基金supported by the National Natural Science Foundation of China(11001037,11102037 and 11290143)the Fundamental Research Funds for the Central Universities
文摘Isoparametric quadrilateral elements are widely used in the finite element method, but the accuracy of the isoparametric quadrilateral elements will drop obviously deteriorate due to mesh distortions. Spline functions have some properties of simplicity and conformality. Two 8-node quadrilateral elements have been developed using the trian- gular area coordinates and the B-net method, which can ex- actly model the quadratic field for both convex and concave quadrangles. Some appropriate examples are employed to evaluate the performance of the proposed elements. The nu- merical results show that the two spline elements can obtain solutions which are highly accurate and insensitive to mesh distortions.
基金supported by the SDUST Spring Bud (2009AZZ021)Taian Science and Technology Development (20112001)
文摘C^1 natural element method （C^1 NEM） is applied to strain gradient linear elasticity, and size effects on mi crostructures are analyzed. The shape functions in C^1 NEM are built upon the natural neighbor interpolation （NNI）, with interpolation realized to nodal function and nodal gradient values, so that the essential boundary conditions （EBCs） can be imposed directly in a Galerkin scheme for partial differential equations （PDEs）. In the present paper, C^1 NEM for strain gradient linear elasticity is constructed, and sev- eral typical examples which have analytical solutions are presented to illustrate the effectiveness of the constructed method. In its application to microstructures, the size effects of bending stiffness and stress concentration factor （SCF） are studied for microspeciem and microgripper, respectively. It is observed that the size effects become rather strong when the width of spring for microgripper, the radius of circular perforation and the long axis of elliptical perforation for microspeciem come close to the material characteristic length scales. For the U-shaped notch, the size effects decline obviously with increasing notch radius, and decline mildly with increasing length of notch.
基金This research was supported by the National Natural Science Foundation of China (10571053)Scientific Research Fund of Hunan Provincial Education Department (0513039)the Special Funds of State Major Basic Research Projects (G1999032804)
文摘This article will combine the finite element method, the interpolated coefficient finite element method, the eigenfunction expansion method, and the search-extension method to obtain the multiple solutions for semilinear elliptic equations. This strategy not only grently reduces the expensive computation, but also is successfully implemented to obtain multiple solutions for a class of semilinear elliptic boundary value problems with non-odd nonlinearity on some convex or nonconvex domains. Numerical solutions illustrated by their graphics for visualization will show the efficiency of the approach.
基金Acknowledgements This study was supported by The National Basic Research Program of China （Grant No. 2015CB453103）, the Strategic Priority Research Program of the Chinese Academy of Sciences （Grant No. XDB14020100） and the National Natural Science Foundation of China （Grant Nos. 21477150 and 21321004）.
文摘We assessed the contamination levels of Mn, Zn, Cr, Cu, Ni, Pb, As and Hg and the risks posed by these potentially harmful elements in top-soils around a municipal solid waste incinerator （MSWI）. We collected 20 soil samples, with an average pH of 8.1, and another fly ash sample emitted from the MSWI to investigate the concentrations of these elements in soils. We determined the concentrations of these elements by inductively coupled plasma-optical emission spectrometer （ICP-OES）, except for Hg, which we measured by AF-610B atomic fluorescence spectrometer （AFS）. We assessed the risks of these elements through the use of geoaccumulation index （/geo）, potential ecological risk index （R/）, hazard quotient （HQi） and cancer risk （Riski）. The results showed that concentrations of potentially harmful elements in soil were influenced by the wind direction, and the concentrations of most elements were higher in the area northwest of the MSWI, compared with the area southeast of the incinerator, with the exception of As; these results were in accordance with those results acquired from our contour maps. According to the I^o values, some soil samples were clearly polluted by Hg emissions. However, the health risk assessment indicated that the concentrations of Hg and other elements in soil did not pose non-carcinogenic risks to the local populations. This was also the case for the carcinogenic risks posed by As Cr and Ni. The carcinogenic risk posed by As was higher in the range 6.49 × 10 -9.58 × 10 -6, but this was still considered to be an acceptable level of risk.
基金This work is supported by National Natural Science Foundations of China under Project(No.11571102)。
文摘In this paper we extend the idea of interpolated coefficients for a semilinear problem to the quadratic triangular finite volume element method.At first we introduce quadratic triangular finite volume element method with interpolated coefficients for a boundary value problem of semilinear elliptic equation.Next we derive convergence estimate in H1-norm,L2-norm and L¥-norm,respectively.Finally an example is given to illustrate the effectiveness of the proposed method.
文摘The aim of this paper is to lay a algebraic geometry foundation for constructing smoothing interpolants on curved side element. Some interpolation theorems in polynomial space are given. The main results effectively for CAGD are presented.
基金This work is supported in part by the National Science Foundation of China （11271145）, the Foundation for Talent Introduction of Guangdong Provincial University, the Specialized Research Fund for the Doctoral Program of Higher Education （20114407110009）, and the Project of Department of Education of Guangdong Province （2012KJCX0036）. It is also supported by the Scientific Research Fund of Hunan Provincial Education Department （12A050） and Hunan Science and Technology Project （No.2011TP4005-8）. The authors express their thanks to the referees for their helpful suggestions, which led to improvements of the presentation.
文摘In this paper we extend the idea of interpolated coefficients for a semilinear problem to the triangular finite volume element method. We first introduce triangular finite volume element method with interpolated coefficients for a boundary value problem of semilinear elliptic equation. We then derive convergence estimate in Hi-norm, L2-norm and L∞-norm, respectively. Finally an example is given to illustrate the effectiveness of the proposed method.
文摘The aim of this paper is to provide a local superconvergence analysis for ined finite element methods of Poission equation. We shall prove that if p is smmoth enough in a local regionΩ0Ω1Ω and rectangular mesh is imposed onΩ1, then local superconvergence for are expected. Thus, by post-processing operators P and we have obtained the follwing local superconvergence error estimate:
