The main aim of this paper is to have an accurate analysis on the famous Adini＇s element for the second order problems under to the anisotropic meshes. We firstly show that the interpolation of Adini＇s element satis...The main aim of this paper is to have an accurate analysis on the famous Adini＇s element for the second order problems under to the anisotropic meshes. We firstly show that the interpolation of Adini＇s element satisfy the anisotropic property. Then the optimal error estimate is obtained without the regularity assumption on the meshes.展开更多
In this paper,we develop a correction operator for the canonical interpolation operator of the Adini element.We use this new correction operator to analyze the discrete eigenvalues of the Adini element method for the ...In this paper,we develop a correction operator for the canonical interpolation operator of the Adini element.We use this new correction operator to analyze the discrete eigenvalues of the Adini element method for the fourth order elliptic eigenvalue problem in the three dimensions.We prove that the discrete eigenvalues are smaller than the exact ones.展开更多
In this paper, we consider the solution of the biharmonic equation using Adini nonconforming finite element, and report new results of the asymptotic error expansions of the interpolation error functionals and nonconf...In this paper, we consider the solution of the biharmonic equation using Adini nonconforming finite element, and report new results of the asymptotic error expansions of the interpolation error functionals and nonconforming remainder. These expansions are used to develop two extrapolation formulas and a series of sharp error estimates. Finally, the numerical results have verified the extrapolation theory.展开更多
n this papers the asymptotic error expansions of Adini's element for the secondorder imhomogeneous Neumann problem are given and the superconvergence estimations are obtained. Moreover, a numerical example to supp...n this papers the asymptotic error expansions of Adini's element for the secondorder imhomogeneous Neumann problem are given and the superconvergence estimations are obtained. Moreover, a numerical example to support our theoreticalanalysis is reported.展开更多
It is proved that the so-called a set of 12-parameter rectangular plate elements with high accuracy constructed by using double set parameter method and undetermined method are, in fact, the same one; the real shape f...It is proved that the so-called a set of 12-parameter rectangular plate elements with high accuracy constructed by using double set parameter method and undetermined method are, in fact, the same one; the real shape function space is nothing but the Adini＇s element＇s, which has nothing to do with the other high degree terms and leads to a new method for constructing the high accuracy plate elements. This fact has never been seen for other conventional and unconventional, conforming and nonconforming rectangular plate elements, such as Quasi-conforming elements, generalized conforming elements and other double set parameter finite elements. Moreover, such kind of rectangular elements can not be constructed by the conventional finite element methods.展开更多
The main aim of this paper is to study the local anisotropic interpolation error estimates. We show that the interpolation of a nonconforming element satisfy the anisotropic property for both the second and fourth ord...The main aim of this paper is to study the local anisotropic interpolation error estimates. We show that the interpolation of a nonconforming element satisfy the anisotropic property for both the second and fourth order problems.展开更多
基金the Henan Natural Science Foundation(072300410320)the Henan Education Department Foundational Study Foundation(200510460311)
文摘The main aim of this paper is to have an accurate analysis on the famous Adini＇s element for the second order problems under to the anisotropic meshes. We firstly show that the interpolation of Adini＇s element satisfy the anisotropic property. Then the optimal error estimate is obtained without the regularity assumption on the meshes.
基金supported by National Natural Science Foundation of China (GrantNo.10971005)A Foundation for the Author of National Excellent Doctoral Dissertation of PR China (GrantNo.200718)+1 种基金supported in part by National Natural Science Foundation of China Key Project (Grant No.11031006)the Chinesisch-Deutsches Zentrum Project (Grant No.GZ578)
文摘In this paper,we develop a correction operator for the canonical interpolation operator of the Adini element.We use this new correction operator to analyze the discrete eigenvalues of the Adini element method for the fourth order elliptic eigenvalue problem in the three dimensions.We prove that the discrete eigenvalues are smaller than the exact ones.
文摘In this paper, we consider the solution of the biharmonic equation using Adini nonconforming finite element, and report new results of the asymptotic error expansions of the interpolation error functionals and nonconforming remainder. These expansions are used to develop two extrapolation formulas and a series of sharp error estimates. Finally, the numerical results have verified the extrapolation theory.
文摘n this papers the asymptotic error expansions of Adini's element for the secondorder imhomogeneous Neumann problem are given and the superconvergence estimations are obtained. Moreover, a numerical example to support our theoreticalanalysis is reported.
文摘It is proved that the so-called a set of 12-parameter rectangular plate elements with high accuracy constructed by using double set parameter method and undetermined method are, in fact, the same one; the real shape function space is nothing but the Adini＇s element＇s, which has nothing to do with the other high degree terms and leads to a new method for constructing the high accuracy plate elements. This fact has never been seen for other conventional and unconventional, conforming and nonconforming rectangular plate elements, such as Quasi-conforming elements, generalized conforming elements and other double set parameter finite elements. Moreover, such kind of rectangular elements can not be constructed by the conventional finite element methods.
文摘The main aim of this paper is to study the local anisotropic interpolation error estimates. We show that the interpolation of a nonconforming element satisfy the anisotropic property for both the second and fourth order problems.
