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CONSERVATIVE CONFORMING AND NONCONFORMING VEMS FOR FOURTH ORDER NONLINEAR SCHRODINGER EQUATIONS WITH TRAPPED TERM: 《Journal of Computational Mathematics》2024年第2期454-499,共46页Meng Li Jikun Zhao Zhongchi Wang Shaochun Chen; supported by the NSF of China(Grant Nos.11801527,11701522,11771163,11671160,1191101330);by the China Postdoctoral Science Foundation(Grant No.2018M632791);by the Key Scientific Research Projects of Higher Eduction of Henan(Grant No.19A110034).; This paper aims to construct and analyze the conforming and nonconforming virtual element methods for a class of fourth order nonlinear Schrodinger equations with trapped term.We mainly consider three types of virtual...; 关键词：H^(2)conforming virtual element C^(0)nonconforming virtual element Morleytype nonconforming virtual element Nonlinear Schrodinger equation Conservation Convergence

AN ERROR ANALYSIS METHOD SPP-BEAM AND A CONSTRUCTION GUIDELINE OF NONCONFORMING FINITE ELEMENTS FOR FOURTH ORDER ELLIPTIC PROBLEMS被引量：2: 《Journal of Computational Mathematics》2020年第1期195-222,共28页Jun Hu Shangyou Zhang; Under two hypotheses of nonconforming finite elements of fourth order elliptic problems,we present a side-patchwise projection based error analysis method(SPP-BEAM for short).Such a method is able to avoid both the re...; 关键词：Nonconforming finite element A priori error analysis Biharmonic equation

UNIFORMLY CONVERGENT NONCONFORMING ELEMENT FOR 3-D FOURTH ORDER ELLIPTIC SINGULAR PERTURBATION PROBLEM被引量：1: 《Journal of Computational Mathematics》2014年第6期687-695,共9页Hongru Chen Shaochun Chen; In this paper, using a bubble function, we construct a cuboid element to solve the fourth order elliptic singular perturbation problem in three dimensions. We prove that the nonconforming CO-cuboid element converges i...; 关键词：Nonconforming finite element Singular perturbation problem Uniform errorestimates.

THE BEST L2 NORM ERROR ESTIMATE OF LOWER ORDER FINITE ELEMENT METHODS FOR THE FOURTH ORDER PROBLEM被引量：1: 《Journal of Computational Mathematics》2012年第5期449-460,共12页Jun Hu Zhong-Ci Shi; In the paper, we analyze the L2 norm error estimate of lower order finite element methods for the fourth order problem. We prove that the best error estimate in the L2 norm of the finite element solution is of second ...; 关键词：L2 norm error estimate Energy norm error estimate Conforming Noncon-forming The Kirchhoff plate.

A NEW FINITE ELEMENT APPROXIMATION OF A STATE-CONSTRAINED OPTIMAL CONTROL PROBLEM被引量：6: 《Journal of Computational Mathematics》2009年第1期97-114,共18页Wenbin Liu Wei Gong Ningning Yan; the National Natural Science Foundation of China (No.60474027 and 10771211);the National Basic Research Program under the Grant 2005CB321701; In this paper, we study numerical methods for an optimal control problem with pointwise state constraints. The traditional approaches often need to deal with the deltasingularity in the dual equation, which causes man...; 关键词：Optimal control problem State-constraints Fourth order variational inequalities Nonconforming finite element method.

A POSTERIORI ESTIMATOR OF NONCONFORMING FINITE ELEMENT METHOD FOR FOURTH ORDER ELLIPTIC PERTURBATION PROBLEMS被引量：1: 《Journal of Computational Mathematics》2008年第4期554-577,共24页Shuo Zhang Ming Wang; supported by the National Natural Science Foundation of China (10571006); In this paper, we consider the nonconforming finite element approximations of fourth order elliptic perturbation problems in two dimensions. We present an a posteriori error estimator under certain conditions, and giv...; 关键词：Fourth order elliptic perturbation problems Nonconforming finite elementmethod A posteriori error estimator Adaptive algorithm Local behavior.

A FOURTH ORDER DERIVATIVE-FREE OPERATOR MARCHING METHOD FOR HELMHOLTZ EQUATION IN WAVEGUIDES: 《Journal of Computational Mathematics》2007年第6期719-729,共11页Ya Yan Lu; A fourth-order operator marching method for the Helmholtz equation in a waveguide is developed in this paper. It is derived from a new fourth-order exponential integrator for linear evolution equations. The method imp...; 关键词：Helmholtz equation WAVEGUIDES Dirichlet-to-Neumann map Operator marching.

JACOBI PSEUDOSPECTRAL METHOD FOR FOURTH ORDER PROBLEMS被引量：1: 《Journal of Computational Mathematics》2006年第4期481-500,共20页Zheng-su Wan Ben-yu Guo Zhong-qing Wang; The work of these authors is supported in part by NSF of China, N.10471095, Science Foundation of Shanghai N.04JC14062, Special Funds for Doctorial Authorities of Chinese Education Ministry N.20040270002, Shanghai Leading Academic Discipline Project N.T0401, E-institutes of Shanghai Municipal Education Commission, N.E03004, Special Funds for Major Specialities and Fund N.04DB15 of Shanghai Education Commission.; In this paper, we investigate Jacobi pseudospectral method for fourth order problems. We establish some basic results on the Jacobi-Gauss-type interpolations in non-uniformly weighted Sobolev spaces, which serve as im...; 关键词：Jacobi pseudospectral method Differential equations of fourth order Singular problems.

MODIFIED MORLEY ELEMENT METHOD FOR A FOURTH ORDER ELLIPTIC SINGULAR PERTURBATION PROBLEM被引量：9: 《Journal of Computational Mathematics》2006年第2期113-120,共8页Ming Wang Jin-chao Xu Yu-cheng Hu; The work of the first author was supported by the National Natural Science Foundation of China （10571006）. The work of the second author was supported by National Science Foundation DMS-0209479 and DMS-0215392 and the Changjiang Professorship through Peking University.; This paper proposes a modified Morley element method for a fourth order elliptic singular perturbation problem. The method also uses Morley element or rectangle Morley element, but linear or bilinear approximation of ...; 关键词：Morley element Singular perturbation problem.

NON C^0 NONCONFORMING ELEMENTS FOR ELLIPTIC FOURTH ORDER SINGULAR PERTURBATION PROBLEM被引量：5: 《Journal of Computational Mathematics》2005年第2期185-198,共14页Shao-chunChen Yong-chengZhao Dong-yangShi; In this paper we give a convergence theorem for non C^0 nonconforming finite element to solve the elliptic fourth order singular perturbation problem. Two such kind of elements, a nine parameter triangular element and...

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