In this paper, it is shown that Quasi-Wilson clement possesses a very special property i.e. the consistency error is of order O(h(2)), one order higher than that of Wilson element.
In this paper, a new triangular element （Quasi-Carey element） is constructed by the idea of Specht element. It is shown that this Quasi-Carey element possesses a very special property, i.e., the consistency error is...In this paper, a new triangular element （Quasi-Carey element） is constructed by the idea of Specht element. It is shown that this Quasi-Carey element possesses a very special property, i.e., the consistency error is of order O（h^2）, one order higher than its interpolation error when the exact solution belongs to H^3（Ω）. However, the interpolation error and consistency error of Carey element are of order O（h）. It seems that the above special property has never been seen for other triangular elements for the second order problems.展开更多
Abstract In this paper, we apply EQ1^rot nonconforming finite element to approximate Signorini problem. If 5 the exact solution u EQ1^rot, the error estimate of order O（h） about the broken energy norm is obtained f...Abstract In this paper, we apply EQ1^rot nonconforming finite element to approximate Signorini problem. If 5 the exact solution u EQ1^rot, the error estimate of order O（h） about the broken energy norm is obtained for quadrilateral meshes satisfying regularity assumption and bi-section condition. Furthermore, the superconver- gence results of order EQ1^rot are derived for rectangular meshes. Numerical results are presented to confirm the considered theory.展开更多
A Crank-Nicolson scheme based on nonconforming finite element with moving grids is dis- cussed for a class of parabolic integro-differential equations under anisotropic meshes. The corresponding convergence analysis i...A Crank-Nicolson scheme based on nonconforming finite element with moving grids is dis- cussed for a class of parabolic integro-differential equations under anisotropic meshes. The corresponding convergence analysis is presented and the error estimates are obtained by using the interpolation operator instead of the conventional elliptic projection which is an indispensable tool in the convergence analysis of traditional finite element methods in previous literature.展开更多
The main aim of this paper is to study the nonconforming linear triangular Crouzeix- Raviart type finite element approximation of planar linear elasticity problem with the pure displacement boundary value on anisotrop...The main aim of this paper is to study the nonconforming linear triangular Crouzeix- Raviart type finite element approximation of planar linear elasticity problem with the pure displacement boundary value on anisotropic general triangular meshes satisfying the maximal angle condition and coordinate system condition. The optimal order error estimates of energy norm and L2-norm are obtained, which are independent of lame parameter λ. Numerical results are given to demonstrate the validity of our theoretical analysis.Mathematics subject classification： 65N30, 65N15.展开更多
In this paper, it is proved that the double set parameter rectangular plate elements with geometric symmetry possess a very special convergence property, i.e., the consistency error due to nonconformity is of order O(...In this paper, it is proved that the double set parameter rectangular plate elements with geometric symmetry possess a very special convergence property, i.e., the consistency error due to nonconformity is of order O(h2) which is one order higher than that of ACM element and rectangular generalized conforming element proposed by Y. Q. Long, although all these elements have the same asympotical rate of convergence O(h) in the energy norm. This particular property seems to be never seen before for other nonconforming rectangular plate elements.展开更多
Several quadrilateral shape regular mesh conditions commonly used in the finite element method are proven to be equivalent. Their influence on the finite element interpolation error and the consistency error committe...Several quadrilateral shape regular mesh conditions commonly used in the finite element method are proven to be equivalent. Their influence on the finite element interpolation error and the consistency error committed by nonconforming finite elements are investigated. The effect of the Bi-Section Condition and its extended version (1+α)-Section Condition on the degenerate mesh conditions is also checked. The necessity of the Bi-Section Condition in finite elements is underpinned by means of counterexamples.展开更多
We propose and analyze a new family of nonconforming finite elements for the three-dimensional quad-curl problem.The proposed finite element spaces are subspaces of H(curl),but not of H(grad curl),which are different ...We propose and analyze a new family of nonconforming finite elements for the three-dimensional quad-curl problem.The proposed finite element spaces are subspaces of H(curl),but not of H(grad curl),which are different from the existing nonconforming ones[10,12,13].The well-posedness of the discrete problem is proved and optimal error estimates in discrete H(grad curl)norm,H(curl)norm and L2 norm are derived.Numerical experiments are provided to illustrate the good performance of the method and confirm our theoretical predictions.展开更多
A mixed finite element method is presented for the Biot consolidation problem in poroe-lasticity.More precisely,the displacement is approximated by using the Crouzeix-Raviart nonconforming finite elements,while the fu...A mixed finite element method is presented for the Biot consolidation problem in poroe-lasticity.More precisely,the displacement is approximated by using the Crouzeix-Raviart nonconforming finite elements,while the fuid pressure is approximated by using the node conforming finite elements.The well-posedness of the fully discrete scheme is established,and a corresponding priori error estimate with optimal order in the energy norm is also derived.Numerical experiments are provided to validate the theoretical results.展开更多
In this work,we focus on the conforming and nonconforming leap-frog virtual element methods for the generalized nonlinear Schrodinger equation,and establish their unconditional stability and optimal error estimates.By...In this work,we focus on the conforming and nonconforming leap-frog virtual element methods for the generalized nonlinear Schrodinger equation,and establish their unconditional stability and optimal error estimates.By constructing a time-discrete system,the error between the solutions of the continuous model and the numerical scheme is separated into the temporal error and the spatial error,which makes the spatial error τ-independent.The inverse inequalities in the existing conforming and new constructed nonconforming virtual element spaces are utilized to derive the L^(∞)-norm uniform boundedness of numerical solutions without any restrictions on time-space step ratio,and then unconditionally optimal error estimates of the numerical schemes are obtained naturally.What needs to be emphasized is that if we use the pre-existing nonconforming virtual elements,there is no way to derive the L^(∞)-norm uniform boundedness of the functions in the nonconforming virtual element spaces so as to be hard to get the corresponding inverse inequalities.Finally,several numerical examples are reported to confirm our theoretical results.展开更多
文摘In this paper, it is shown that Quasi-Wilson clement possesses a very special property i.e. the consistency error is of order O(h(2)), one order higher than that of Wilson element.
基金This research is supported by the National Natural Science Foundation of China under Grant No.10671184
文摘In this paper, a new triangular element （Quasi-Carey element） is constructed by the idea of Specht element. It is shown that this Quasi-Carey element possesses a very special property, i.e., the consistency error is of order O（h^2）, one order higher than its interpolation error when the exact solution belongs to H^3（Ω）. However, the interpolation error and consistency error of Carey element are of order O（h）. It seems that the above special property has never been seen for other triangular elements for the second order problems.
基金supported by National Natural Science Foundation of China (Grant Nos.10971203 and 11271340)Research Fund for the Doctoral Program of Higher Education of China (Grant No.20094101110006)
文摘Abstract In this paper, we apply EQ1^rot nonconforming finite element to approximate Signorini problem. If 5 the exact solution u EQ1^rot, the error estimate of order O（h） about the broken energy norm is obtained for quadrilateral meshes satisfying regularity assumption and bi-section condition. Furthermore, the superconver- gence results of order EQ1^rot are derived for rectangular meshes. Numerical results are presented to confirm the considered theory.
基金supported in part by the National Basic Research Program (2007CB814906)the National Natural Science Foundation of China (10471103 and 10771158)+2 种基金Social Science Foundation of the Ministry of Education of China (Numerical methods for convertible bonds, 06JA630047)Tianjin Natural Science Foundation (07JCYBJC14300)the National Science Foundation under Grant No. EAR-0934747
文摘This article summarizes our recent work on uniform error estimates for various finite elementmethods for time-dependent advection-diffusion equations.
基金This research is supported by the National Natural Science Foundation of China under Grant Nos. 10671184 and 10971203.
文摘A Crank-Nicolson scheme based on nonconforming finite element with moving grids is dis- cussed for a class of parabolic integro-differential equations under anisotropic meshes. The corresponding convergence analysis is presented and the error estimates are obtained by using the interpolation operator instead of the conventional elliptic projection which is an indispensable tool in the convergence analysis of traditional finite element methods in previous literature.
基金Acknowledgments. This work was supported by National Natural Science Foundation of China （No. 10971203）, Specialized Research Fund for the Doctoral Program of Higher Education （No. 20094101110006）, the Educational Department Foundation of Henan Province of China （No.2009B110013）.
文摘The main aim of this paper is to study the nonconforming linear triangular Crouzeix- Raviart type finite element approximation of planar linear elasticity problem with the pure displacement boundary value on anisotropic general triangular meshes satisfying the maximal angle condition and coordinate system condition. The optimal order error estimates of energy norm and L2-norm are obtained, which are independent of lame parameter λ. Numerical results are given to demonstrate the validity of our theoretical analysis.Mathematics subject classification： 65N30, 65N15.
基金This research is supported by the National Natural Science Foundation of China!19871079Natural Science Foundation of Henan P
文摘In this paper, it is proved that the double set parameter rectangular plate elements with geometric symmetry possess a very special convergence property, i.e., the consistency error due to nonconformity is of order O(h2) which is one order higher than that of ACM element and rectangular generalized conforming element proposed by Y. Q. Long, although all these elements have the same asympotical rate of convergence O(h) in the energy norm. This particular property seems to be never seen before for other nonconforming rectangular plate elements.
文摘Several quadrilateral shape regular mesh conditions commonly used in the finite element method are proven to be equivalent. Their influence on the finite element interpolation error and the consistency error committed by nonconforming finite elements are investigated. The effect of the Bi-Section Condition and its extended version (1+α)-Section Condition on the degenerate mesh conditions is also checked. The necessity of the Bi-Section Condition in finite elements is underpinned by means of counterexamples.
基金supported in part by the National Natural Science Foundation of China grant NSFC 12131005.
文摘We propose and analyze a new family of nonconforming finite elements for the three-dimensional quad-curl problem.The proposed finite element spaces are subspaces of H(curl),but not of H(grad curl),which are different from the existing nonconforming ones[10,12,13].The well-posedness of the discrete problem is proved and optimal error estimates in discrete H(grad curl)norm,H(curl)norm and L2 norm are derived.Numerical experiments are provided to illustrate the good performance of the method and confirm our theoretical predictions.
基金supported by the Guangdong Basic and Applied Basic Research Foundation(Grant No.2020A1515011032)The work of M.Cai is supported in part by the NIH-BUILD(Grant No.UL1GM118973)+2 种基金by the NIH-RCMI(Grant No.U54MD013376)the National Science Foundation awards(Grant Nos.1700328,1831950)The work of L.Zhong is supported by the National Natural Science Foundation of China(Grant No.12071160)。
文摘A mixed finite element method is presented for the Biot consolidation problem in poroe-lasticity.More precisely,the displacement is approximated by using the Crouzeix-Raviart nonconforming finite elements,while the fuid pressure is approximated by using the node conforming finite elements.The well-posedness of the fully discrete scheme is established,and a corresponding priori error estimate with optimal order in the energy norm is also derived.Numerical experiments are provided to validate the theoretical results.
基金supported by the NSF of China(Grant Nos.11801527,11701522,11771163,12011530058,11671160,1191101330)by the China Postdoctoral Science Foundation(Grant Nos.2018M632791,2019M662506).
文摘In this work,we focus on the conforming and nonconforming leap-frog virtual element methods for the generalized nonlinear Schrodinger equation,and establish their unconditional stability and optimal error estimates.By constructing a time-discrete system,the error between the solutions of the continuous model and the numerical scheme is separated into the temporal error and the spatial error,which makes the spatial error τ-independent.The inverse inequalities in the existing conforming and new constructed nonconforming virtual element spaces are utilized to derive the L^(∞)-norm uniform boundedness of numerical solutions without any restrictions on time-space step ratio,and then unconditionally optimal error estimates of the numerical schemes are obtained naturally.What needs to be emphasized is that if we use the pre-existing nonconforming virtual elements,there is no way to derive the L^(∞)-norm uniform boundedness of the functions in the nonconforming virtual element spaces so as to be hard to get the corresponding inverse inequalities.Finally,several numerical examples are reported to confirm our theoretical results.
