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An accurate a posteriori error estimator for the Steklov eigenvalue problem and its applications

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Science China Mathematics 2021年第3期64卷 623-638页

作者： Fei Xu qiumei huang Beijing Institute for Scientific and Engineering Computing Faculty of ScienceBeijing University of TechnologyBeijing 100124China

In this paper, a type of accurate a posteriori error estimator is proposed for the Steklov eigenvalue problem based on the complementary approach, which provides an asymptotic exact estimate for the approximate eigenpair. Besides, we design a type of cascadic adaptive finite element method for the Steklov eigenvalue problem based on the proposed a posteriori error estimator. In this new cascadic adaptive scheme, instead of solving the Steklov eigenvalue problem in each adaptive space directly, we only need to do some smoothing steps for linearized boundary value problems on a series of adaptive spaces and solve some Steklov eigenvalue problems on a low dimensional space. Furthermore, the proposed a posteriori error estimator provides the way to refine meshes and control the number of smoothing steps for the cascadic adaptive method. Some numerical examples are presented to validate the efficiency of the algorithm in this paper.

关键词： Steklov eigenvalue problem a posteriori error estimator cascadic multigrid method adaptive finite element method complementary method

EXPONENTIAL TIME DIFFERENCING-PADE FINITE ELEMENT METHOD FOR NONLINEAR CONVECTION-DIFFUSION-REACTION EQUATIONS WITH TIME CONSTANT DELAY

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Journal of Computational Mathematics 2023年第3期41卷 370-394页

作者： Haishen Dai qiumei huang Cheng Wang School of Mathematics Faculty of ScienceBeijing University of TechnologyBeijing 100124China Department of Mathematics University of MassachusettsNorth DartmouthMA 02747USA

In this paper,ETD3-Padéand ETD4-PadéGalerkin finite element methods are proposed and analyzed for nonlinear delayed convection-diffusion-reaction equations with Dirichlet boundary *** ETD-based RK is used for time integration of the corresponding *** overcome a well-known difficulty of numerical instability associated with the computation of the exponential operator,the Padéapproach is used for such an exponential operator approximation,which in turn leads to the corresponding ETD-Padé*** unconditional L^(2) numerical stability is proved for the proposed numerical schemes,under a global Lipshitz continuity *** addition,optimal rate error estimates are provided,which gives the convergence order of O(k^(3)+h^(r))(ETD3-Padé)or O(k^(4)+h^(r))(ETD4-Padé)in the L^(2)norm,*** experiments are presented to demonstrate the robustness of the proposed numerical schemes.

关键词： Nonlinear delayed convection diffusion reaction equations ETD-Pad´e scheme Lipshitz continuity L^(2)stability analysis Convergence analysis and error estimate

Numerical Investigations of a Class of Biological Models on Unbounded Domain

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Numerical Mathematics(Theory,Methods and Applications) 2019年第1期12卷 169-186页

作者： qiumei huang Dongfang Li Jiwei Zhang Beijing Institute for Scientific and Engineering Computing Beijing University of TechnologyBeijing 100124China School of Mathematics and Statistics Huazhong University of Science and TechnologyWuhan 430074China Hubei Key Laboratoryof Engineering Modeling and Scientific Computing Huazhong University of Science and TechnologyWuhan 430074China Beijing Computational Science Research Center Beijing1000193China

This paper is concerned with numerical computations of a class of biologi-cal models on unbounded spatial *** overcome the unboundedness of spatial domain,we first construct efficient local absorbing boundary conditions(LABCs)to re-formulate the Cauchy problem into an initial-boundary value(IBV)*** that,we construct a linearized finite difference scheme for the reduced IVB problem,and provide the corresponding error estimates and stability *** delay-dependent dynamical properties on the Nicholson’s blowflies equation and the Mackey-Glass equa-tion are numerically ***,numerical examples are given to demonstrate the efficiency of our LABCs and theoretical results of the numerical scheme.

关键词： Biological models artificial boundary method absorbing boundary conditions finite difference method stability,convergence

LOCAL SUPERCONVERGENCE OF CONTINUOUS GALERKIN SOLUTIONS FOR DELAY DIFFERENTIAL EQUATIONS OF PANTOGRAPH TYPE

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Journal of Computational Mathematics 2016年第2期34卷 186-199页

作者： Xiuxiu Xu qiumei huang Hongtao Chen Beijing Institute for Scientific and Engineering Computing Beijing University of Technology Beijing 100124 China School of Mathematical Sciences and Fujian Provincial Key Laboratory on Mathematical Modeling and High Performance Scientific Computing Xiamen University Xiamen 361005 China

This paper is concerned with the superconvergent points of the continuous Galerkin solutions for delay differential equations of pantograph type. We prove the local nodal superconvergence of continuous Galerkin solutions under uniform meshes and locate all the superconvergent points based on the supercloseness between the continuous Galerkin solution U and the interpolation Hhu of the exact solution u. The theoretical results are illustrated by numerical examples.

关键词： Pantograph delay differential equations Uniform mesh Continuous Galerkinmethods Supercloseness Superconvergence.

家庭协作干预对慢性胃炎并发胃黏膜萎缩糜烂患者胃肠道症状、负性情绪及生活质量的影响

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中外医疗 2024年第9期43卷 120-123页

作者：陈碧珍赵瑜黄秋美福建省地质医院(福建省华侨医院)内科福建福州350019

目的研讨家庭协作干预对慢性胃炎并发胃黏膜萎缩糜烂患者胃肠道症状、负性情绪及生活质量的影响。方法随机选取2020年3月—2023年3月福建省地质医院确诊为慢性胃炎并发胃黏膜萎缩糜烂的180例患者为研究对象,按照随机数表法分为两组,每... 详细信息

目的研讨家庭协作干预对慢性胃炎并发胃黏膜萎缩糜烂患者胃肠道症状、负性情绪及生活质量的影响。方法随机选取2020年3月—2023年3月福建省地质医院确诊为慢性胃炎并发胃黏膜萎缩糜烂的180例患者为研究对象,按照随机数表法分为两组,每组90例。对照组予以常规护理,观察组基于对照组开展家庭协作干预,对比两组干预前后的胃肠道症状、负性情绪以及生活质量。结果干预后,观察组胃肠道症状评估量表得分为(43.28±4.94)分,低于对照组的(45.81±5.11)分,差异有统计学意义(t=3.376,P<0.001)。干预后,观察组汉密尔顿抑郁量表、汉密尔顿焦虑量表得分均低于对照组,差异有统计学意义(P均<0.05)。干预后,观察组世界卫生组织生活质量量表4个维度(心理功能、环境功能、社会功能及生理功能)得分相比对照组均更高,差异有统计学意义(P均<0.05)。结论家庭协作干预能够有效改善慢性胃炎并发胃黏膜萎缩糜烂患者的胃肠道症状,减轻患者的负性情绪,改善患者的生活质量。

关键词：慢性胃炎胃黏膜萎缩糜烂家庭协作干预胃肠道症状

Exponential Time Differencing Schemes for the Peng-Robinson Equation of State with Preservation of Maximum Bound Principle

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Advances in Applied Mathematics and Mechanics 2022年第2期14卷 494-527页

作者： qiumei huang Kun Jiang Jingwei Li College of Mathematics Faculty of ScienceBeijing University of TechnologyBeijing 100124China Beijing Institute for Scientific and Engineering Computing Beijing University of TechnologyBeijing 100124China Laboratory of Mathematics and Complex Systems and School of Mathematical Science Beijing Normal UniversityBeijing 100875China

The Peng-Robison equation of state,one of the most extensively applied equations of state in the petroleum industry and chemical engineering,has an excel-lent appearance in predicting the thermodynamic properties of a wide variety of *** has been a great challenge on how to design numerical schemes with preser-vation of mass conservation and energy dissipation *** on the exponential time difference combined with the stabilizing technique and added Lagrange multi-plier enforcing the mass conservation,we develop the efﬁcientﬁrst-and second-order numerical schemes with preservation of maximum bound principle(MBP)to solve the single-component two-phase diffuse interface model with Peng-Robison equation of *** analyses as well as energy stability are also *** two-dimensional and three-dimensional experiments are performed to verify these theo-retical results.

关键词： Peng-Robinson equation of state diffuse interface model maximum bound principle exponential time differencing Lagrange multiplier

Discontinuous Galerkin Methods for Multi-Pantograph Delay Differential Equations

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Advances in Applied Mathematics and Mechanics 2020年第1期12卷 189-211页

作者： Kun Jiang qiumei huang Xiuxiu Xu College of Applied Sciences Beijing University of TechnologyBeijing 100124China School of Mathematical Sciences Anhui UniversityHefei 230031China

In this paper,the discontinuous Galerkin method is applied to solve the multi-pantograph delay differential *** analyze the optimal global convergence and local superconvergence for smooth solutions under uniform *** to the initial singularity of the forcing term f,solutions of multi-pantograph delay differential equations are *** obtain the relevant global convergence and local superconvergence for weakly singular solutions under graded *** numerical examples are provided to illustrate our theoretical results.

关键词： Multi-pantograph discontinuous Galerkin method global convergence local superconvergence,weakly singular graded meshes

石墨烯/胶粉复合改性沥青储存稳定性和流变性能研究

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市政技术 2024年第9期42卷 208-213页

作者：方志江滕友金黄秋媚黄昌介贵州交通建设集团有限公司贵州贵阳550002 广西交科集团有限公司广西壮族自治区南宁530007

为研究石墨烯对胶粉改性沥青储存稳定性和流变性能的影响,在胶粉掺量为基质沥青质量的20%的前提下,掺入不同掺量的石墨烯制备石墨烯/胶粉复合改性沥青,并对其开展储存稳定性试验和动态黏弹性力学试验,全面评价石墨烯/胶粉复合改性沥青... 详细信息

为研究石墨烯对胶粉改性沥青储存稳定性和流变性能的影响,在胶粉掺量为基质沥青质量的20%的前提下,掺入不同掺量的石墨烯制备石墨烯/胶粉复合改性沥青,并对其开展储存稳定性试验和动态黏弹性力学试验,全面评价石墨烯/胶粉复合改性沥青的储存稳定性和流变性能。试验结果表明:石墨烯最佳掺量为基质沥青质量的1.0%,且0.5%、1.0%掺量的石墨烯能够显著改善胶粉改性沥青的储存稳定性、高温性能和疲劳性能,但随着石墨烯掺量增加到1.5%,石墨烯/胶粉复合改性沥青的各项性能均有所下降,因此石墨烯掺量不宜过高。该研究成果可为胶粉改性沥青的性能改善和复合改性提供技术路线和一定的参考。

关键词：道路工程石墨烯胶粉改性沥青复合改性储存稳定性流变性能

Preparation and photocatalytic activity of Fe3O4@SiO2@ZnO:La

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Journal of Rare Earths 2020年第12期38卷 1288-1296页

作者： Xiaowei Lv Wenyi huang Xingcheng Ding Jiangwei He qiumei huang Jialin Tan Hao Cheng Jun Feng Lijun Li Guangxi Key Laboratory of Green Processing of Sugar Resources College of Biological and Chemical EngineeringGuangxi University of Science and TechnologyLiuzhou 545006China Zhejiang Runtu Co. Ltd.Shangyu 312300China

In this study,Fe3 O4@SiO2@ZnO:La microspheres were successfully *** microspheres have the advantages of both ZnO doped with La and the Fe3 O4@SiO2 structure such that the former improves the photocatalytic activity of ZnO and the latter can be *** X-ray diffraction(XRD),a field emission scanning electron microscope(SEM),a field emission transmission electron microscope(TEM),X-ray photoelectron spectroscopy(XPS),and a vibrating sample magnetometer(VSM)were used to characterize Fe3 O4@SiO2@ZnO:La *** orange was used as the model molecule to study the effect of the Zn2+concentration and the doping amount of La on the photocatalytic activity of Fe3 O4@SiO2@ZnO:La *** show that in the synthesis of Fe3 O4@SiO2@ZnO:La microspheres,photocatalytic activity of the microspheres is enhanced first and weakened later with the increase of Zn2+*** the La doping process,the photocatalytic activity of Fe3 O4@SiO2@ZnO:La microspheres is enhanced with the increase in the La doping *** magnetic photocatalysts not only have high photocatalytic activity,but also can be *** being reused five times,the photocatalyst’s degradation rate of methyl orange is still as high as 81%,which shows that magnetic photocatalysts have prospective wider applications in photocatalytic degradation of dye wastewater.

关键词： Fe3O4@SiO2 ZnO:La Photocatalysis Reuse Rare earths