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CONSERVATIVE CONFORMING AND NONCONFORMING VEMS FOR FOURTH ORDER NONLINEAR SCHRODINGER EQUATIONS WITH TRAPPED TERM

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Journal of Computational Mathematics 2024年第2期42卷 454-499页

作者： Meng Li Jikun Zhao Zhongchi Wang shaochun chen School of Mathematics and Statistics Zhengzhou UniversityZhengzhou 450001China School of Computer Science and Engineering Beihang universityBeijing 100083China

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 *** mainly consider three types of virtual elements,including H^(2) conforming virtual element,C^(0) nonconforming virtual element and Morley-type nonconforming virtual *** fully discrete schemes are constructed by virtue of virtual element methods in space and modified Crank-Nicolson method in *** prove the mass and energy conservation,the boundedness and the unique solvability of the fully discrete *** introducing a new type of the Ritz projection,the optimal and unconditional error estimates for the fully discrete schemes are presented and ***,two numerical examples are investigated to confirm our theoretical analysis.

关键词： H^(2)conforming virtual element C^(0)nonconforming virtual element Morleytype nonconforming virtual element Nonlinear Schrodinger equation Conservation Convergence

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耐药淋病奈瑟球菌的备选治疗方案

中华皮肤科杂志 2024年第3期57卷 272-275页

作者：张瑾陈绍椿尹跃平中国医学科学院、北京协和医学院皮肤病医院参比实验室、中国疾病预防控制中心性病控制中心南京210042

头孢曲松是治疗淋病主要的一线用药,但淋球菌对多种抗生素广泛耐药。为减缓淋球菌的耐药,亟需寻找有效的备选治疗方案。本文从联合疗法、老药新用和新药研发3个方面综述可能有效的抗淋球菌药物。

关键词：淋病淋病奈瑟球菌抗药性,细菌备选治疗方案治疗策略

UNIFORMLY CONVERGENT NONCONFORMING ELEMENT FOR 3-D FOURTH ORDER ELLIPTIC SINGULAR PERTURBATION PROBLEM

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Journal of Computational Mathematics 2014年第6期32卷 687-695页

作者： Hongru chen shaochun chen College of Science Henan University of Technology Zhengzhou 450001 China Department of Mathematics Zhengzhou University Zhengzhou 450001 China

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... 详细信息

关键词： Nonconforming finite element Singular perturbation problem Uniform errorestimates.

浙江何氏妇科治疗子宫内膜异位症不孕经验介绍

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新中医 2024年第10期56卷 184-187页

作者：鲁颖晔陈少春(指导) 嘉兴市妇幼保健院浙江嘉兴314000 杭州市中医院浙江杭州310007

总结介绍浙江何氏妇科治疗子宫内膜异位症不孕的临证经验。何氏妇科认为,子宫内膜异位症不孕的病因病机为本虚标实,本虚与脾肾相关,标实与瘀、滞相关,虚实夹杂。在治疗上有以下特色:周期辨治,病证结合;标本缓急,中病即止;阴阳并举,寒温... 详细信息

总结介绍浙江何氏妇科治疗子宫内膜异位症不孕的临证经验。何氏妇科认为,子宫内膜异位症不孕的病因病机为本虚标实,本虚与脾肾相关,标实与瘀、滞相关,虚实夹杂。在治疗上有以下特色:周期辨治,病证结合;标本缓急,中病即止;阴阳并举,寒温有度;辨别虚实,固护后天;内外合治,增强疗效。用药特色主要有:小方药对,简便显效;巧用虫类,粉剂增效。

关键词：子宫内膜异位症不孕何氏妇科

ESTIMATIONS OF THE CONSTANTS IN INVERSE INEQUALITIES FOR FINITE ELEMENT FUNCTIONS

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Journal of Computational Mathematics 2013年第5期31卷 522-531页

作者： shaochun chen Jikun Zhao Department of Mathematics Zhengzhou University Zhengzhou 450001 China

In this paper, we estimate the constants in the inverse inequalities for the finite ele- ment functions. Furthermore, we obtain the least upper bounds of the constants in inverse inequalities for the low-order finite element functions. Such explicit estimates of the con- stants can be used as computable error bounds for the finite element method.

关键词： nverse inequality Finite element function Bound of the constant.

UNIFORMLY CONVERGENT NONCONFORMING TETRAHEDRAL ELEMENT FOR DARCY-STOKES PROBLEM

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Journal of Computational Mathematics 2019年第1期37卷 130-150页

作者： Lina Dong shaochun chen Department of Mathematics Henan Finance UniversityZhengzhou 450046China Department of Mathematics Zhengzhou UniversityZhengzhou 450001China

In this paper,we construct a tetrahedral element named DST20 for the three dimensional Darcy-Stokes problem,which reduces the degrees of velocity in [30].The finite element space Vh for velocity is H(div)-conforming,i.e.,the normal component of a function in Vh is continuous across the element boundaries,meanwhile the tangential component of a function in Vh is average continuous across the element boundaries,hence Vh is H^1- average *** prove that this element is uniformly convergent with respect to the perturbation constant s for the Darcy-Stokes *** the same time,we give a discrete de Rham complex corresponding to DST20 element.

关键词： Darcy-Stokes problem Mixed finite elements Tetrahedral element Uniformly convergent

CONVERGENCE OF A MIXED FINITE ELEMENT FOR THE STOKES PROBLEM ON ANISOTROPIC MESHES

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Journal of Computational Mathematics 2008年第5期26卷 740-755页

作者： Qingshan Li Huixia Sun shaochun chen Department of Mathematics Zhengzhou University Zhengzhou 450001 China College of Science Henan University of Technology Zhengzhou 450001 China

The main aim of this paper is to study the convergence properties of a low order mixed finite element for the Stokes problem under anisotropic meshes. We discuss the anisotropic convergence and superconvergence independent of the aspect ratio. Without the shape regularity assumption and inverse assumption on the meshes, the optimal error estimates and natural superconvergence at central points are obtained. The global superconvergence for the gradient of the velocity and the pressure is derived with the aid of a suitable postprocessing method. Furthermore, we develop a simple method to obtain the superclose properties which improves the results of the previous works .

关键词： Mixed finite element Shape regularity assumption and 65N30 Stokes problem Anisotropic meshes Superconvergence inverse assumption.

Interpolation theory of anisotropic finite elements and applications

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Science China Mathematics 2008年第8期51卷 1361-1375页

作者： chen shaochun XIAO LiuChao Department of Mathematics Zhengzhou UniversityZhengzhou 450052China

Interpolation theory is the foundation of finite element *** this paper,after reviewing some existed interpolation theorems of anisotropic finite element methods,we present a new way to analyse the interpolation error... 详细信息

关键词： interpolation theory anisotropic finite elements Newton’s formula divided difference 65N30

Uniformly convergent H(div)-conforming rectangular elements for Darcy-Stokes problem

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Science China Mathematics 2013年第12期56卷 2723-2736页

作者： chen shaochun DONG LiNa QIAO ZhongHua Department of Mathematics Zhengzhou University Department of Mathematics Henan Institute of Education Department of Applied Mathematics The Hong Kong Polytechnic University

We consider a singular perturbation problem which describes 2D Darcy-Stokes flow. An H（div）- conforming rectangular element, DS-R14, is proposed and analyzed first. This element has 14 degrees of freedom for velocity and is proved to be uniformly convergent with respect to perturbation constant. We then simplify this element to get another H（div）-conforming rectangular element, DS-R12, which has 12 degrees of freedom for velocity. The uniform convergence is also obtained for this element. Finally, we construct a de Rham complex corresponding to DS-R12 element.

关键词： Darcy-Stokes problem H(div)-conforming rectangular elements uniform convergence