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ERROR REduCTION, CONVERGENCE AND OPTIMALITY FOR ADAPTIVE MIXED FINITE ELEMENT METHODS FOR DIFFUSION EQUATIONS

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Journal of Computational Mathematics 2012年第5期30卷 483-503页

作者： shaohong du Xiaoping Xie School of Science Chongqing Jiaotong UniversityChongqing 400074China School of Mathematics Sichuan UniversityChengdu 610064China

Error reduction, convergence and optimality are analyzed for adaptive mixed finite element methods （AMFEM） for diffusion equations without marking the oscillation of data. Firstly, the quasi-error, i.e. the sum of the stress variable error and the scaled error estimator, is shown to reduce with a fixed factor between two successive adaptive loops, up to an oscillation. Secondly, the convergence of AMFEM is obtained with respect to the quasi-error plus the divergence of the flux error. Finally, the quasi-optimal convergence rate is established for the total error, i.e. the stress variable error plus the data oscillation.

关键词： Adaptive mixed finite element method Error reduction Convergence Quasi-optimal convergence rate

Convergence of an adaptive mixed finite element method for convection-diffusion-reaction equations

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Science China Mathematics 2015年第6期58卷 1327-1348页

作者： du shaohong XIE XiaoPing School of Science Chongqing Jiaotong University Beijing Computational Science Research Center School of Mathematics Sichuan University

We prove the convergence of an adaptive mixed finite element method(AMFEM) for(nonsymmetric) convection-diffusion-reaction equations. The convergence result holds for the cases where convection or reaction is not present in convection- or reaction-dominated problems. A novel technique of analysis is developed by using the superconvergence of the scalar displacement variable instead of the quasi-orthogonality for the stress and displacement variables, and without marking the oscillation dependent on discrete solutions and data. We show that AMFEM is a contraction of the error of the stress and displacement variables plus some quantity. Numerical experiments confirm the theoretical results.

关键词： convection instead posteriori marking meshes projection interpolation holds interior satisfy

ON RESIduAL-BASED A POSTERIORI ERROR ESTIMATORS FOR LOWEST-ORDER RAVIART-THOMAS ELEMENT APPROXIMATION TO CONVECTION-DIFFUSION-REACTION EQUATIONS

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Journal of Computational Mathematics 2014年第5期32卷 522-546页

作者： shaohong du Xiaoping Xie School of Science Chongqing Jiaotong University Chongqing 400047 China Beijing Computational Science Research Center Beijing 100084 China School of Mathematics Sichuan University Chengdu 610063 China

A new technique of residual-type a posteriori error analysis is developed for the lowest- order Raviart-Thomas mixed finite element discretizations of convection-diffusion-reaction equations in two- or three-dimension. Both centered mixed scheme and upwind-weighted mixed scheme are considered. The a posteriori error estimators, derived for the stress variable error plus scalar displacement error in L_2-norm, can be directly computed with the solutions of the mixed schemes without any additional cost, and are proven to be reliable. Local efficiency dependent on local variations in coefficients is obtained without any saturation assumption, and holds from the cases where convection or reaction is not present to convection- or reaction-dominated problems. The main tools of the analysis are the postprocessed approximation of scalar displacement, abstract error estimates, and the property of modified Oswald interpolation. Numerical experiments are carried out to support our theoretical results and to show the competitive behavior of the proposed posteriori error estimates.

关键词： Convection-diffusion-reaction equation Centered mixed scheme Upwind-weightedmixed scheme Postproeessed approximation A posteriori error estimators.

Residual-based a posteriori error estimates of nonconforming finite element method for elliptic problems with Dirac delta source terms

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Science China Mathematics 2008年第8期51卷 1440-1460页

作者： du shaohong XIE XiaoPing School of Mathematics Sichuan UniversityChengdu 610064China School of Science Chongqing Jiaotong UniversityChongqiong 400047China Yangtze Center of Mathematics Sichuan UniversityChengdu 610064China

Two residual-based a posteriori error estimators of the nonconforming Crouzeix-Raviart element are derived for elliptic problems with Dirac delta source *** estimator is shown to be reliable and efficient,which yields global upper and lower bounds for the error in piecewise W1,p *** other one is proved to give a global upper bound of the error in *** taking the two estimators as refinement indicators,adaptive algorithms are suggested,which are experimentally shown to attain optimal convergence orders.

关键词： Crouzeix-Raviart element nonconforming FEM a posteriori error estimator longest edge bisection 65N15 65N30 65N50

Hybrid assembly of conducting nanofiber network for ultra-stretchable and highly sensitive conductive hydrogels

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Journal of Materials Science & Technology 2024年第2期169卷 1-10页

作者： Yalei Wang Shulong Zeng shaohong Shi Yuheng Jiang Zhiwei du Bingzhen Wang Xiurong Li State Key Laboratory of Featured Metal Materials and Life-cycle Safety for Composite Structures School of ResourcesEnvironment and MaterialsGuangxi UniversityNanning 530004China State Key Laboratory of Polymer Materials Engineering Polymer Research Institute of Sichuan UniversitySichuan UniversityChengdu 610065China

Conductive hydrogels have attracted extensive attention owing to their promising application prospects in flexible and wearable ***,achieving both high sensitivity and mechanical robustness remains ***,a novel and versatile conductive hydrogel based on the hybrid assem-bly of conductive cellulose nanofiber(CNF)networks has been designed and *** by the templating effect of CNFs and stabilizing effect of negatively charged poly(styrene sulfonate)(PSS),conducting polymer poly(3,4-ethylenedioxythiophene)(PEDOT)was self-organized into three-dimensional nanostructures which constructed a robust conductive network after in-situ oxidative *** unique structure derived from CNF bio-template endowed polyacrylamide(PAM)hydrogels with improved electrical conductivity and excellent mechanical *** a result,the as-fabricated CNF/PEDOT:PSS/PAM hydrogel exhibited an ultimate tensile strain of 1881%and toughness of 3.72 MJ/m^(3),which were 4.07 and 8.27 times higher than the CNF-free hydrogel,*** significantly,the resultant hydrogel sensor showed highly desirable sensing properties,including remarkable sensing range(1100%),high gauge factor(GF=5.16),fast response time(185 ms),and commendable durability,as well as good ***,the hydrogel sensor was able to distinguish subtle physiological activities including phonation and facial expression,and monitor large human body motions such as finger flexion and elbow ***,it was feasible to integrate the strain sensor on the joints of robots to recognize complicated machine motion signals,showing potential in advanced human-machine interactions.

关键词： Strain sensor Cellulose nanofibers PEDOT:PSS Conductive hydrogel Templating method

A Linearized Adaptive Dynamic Diffusion Finite Element Method for Convection-Diffusion-Reaction Equations

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Annals of Applied Mathematics 2023年第3期39卷 323-351页

作者： shaohong du Qianqian Hou Xiaoping Xie School of Mathematics and Statistics Chongqing Jiaotong UniversityChongqing 400074China School of Mathematics Sichuan UniversityChengduSichuan 610064China

In this paper,we consider a modified nonlinear dynamic diffusion(DD)method for convection-diffusion-reaction *** method is free of stabilization parameters and capable of precluding spurious *** develop a reliable and efficient residual-type a posteriori error estimator,which is robust with respect to the diffusivity ***,we propose a linearized adaptive DD algorithm based on the a posteriori ***,we perform numerical experiments to verify the theoretical analysis and the performance of the adaptive algorithm.

关键词： Convection-diffusion-reaction equation dynamical diffusion method residualtype a posteriori error estimator adaptive algorithm

Simulation of wave scattering over a floating platform in the ocean with a coupled CFD-IBM model

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Theoretical & Applied Mechanics Letters 2024年第3期14卷 157-161页

作者： Pengxuan Luo Jingxin Zhang Yongyong Cao shaohong Song School of Naval Architecture Ocean&Civil EngineeringShanghai Jiao Tong UniversityShanghai 200240China MOE Key Laboratory of Hydrodynamics Shanghai Jiao Tong UniversityShanghai 200240China Shanghai city Tou waterway construction Co. LTDShanghai 200092China

A numerical study of linear wave scattering over a floating platform has been simulated by an efficient numericalmodel in this *** non-hydrostatic model is used to simulate the free surface and the uneven *** thesolid body modelling,the immersed boundary method(IBM)is implemented by introducing a virtual boundaryforce into the momentum equations to emulate the boundary *** implementation enhances theability of the model to simulate interactions between waves and floating structures.A numerical case involvingwave interactions with a floating platform is studied to validate the numerical *** simulating the wavepropagation,the numerical model captures the variation of the wave scattering very well,which verifies theperformance of the numerical model and the robust strategy of the IBM.

关键词： Non-hydrostatic model Immersed boundary method Wave structure interaction Floating platform

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梁自由横振动方程的有限差分方法

重庆交通大学学报（自然科学版） 2012年第1期31卷 6-10页

作者：杜绍洪重庆交通大学理学院重庆400074

以简支梁的自由横振动问题为背景,求解一个非稳态四阶线性偏微分方程的初边值问题。通过引进辅助函数组,将四阶问题转化为二阶混合初边值问题。对两个辅助函数和二阶混合初边值问题进行离散并消掉中间变量,对由简支梁两端挠度为零得来... 详细信息

以简支梁的自由横振动问题为背景,求解一个非稳态四阶线性偏微分方程的初边值问题。通过引进辅助函数组,将四阶问题转化为二阶混合初边值问题。对两个辅助函数和二阶混合初边值问题进行离散并消掉中间变量,对由简支梁两端挠度为零得来的二阶偏微分边界条件进行近似处理,构造出求解四阶非稳态线性偏微分方程的差分隐格式。数值实验表明构造的隐格式绝对稳定并且具有很高的精度阶。

关键词：梁横振动方程有限差分方法差分格式的绝对稳定

3D‑Printed Carbon‑Based Conformal Electromagnetic Interference Shielding Module for Integrated Electronics

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Nano-Micro Letters 2024年第5期16卷 87-101页

作者： shaohong Shi Yuheng Jiang Hao Ren Siwen Deng Jianping Sun Fangchao Cheng Jingjing Jing Yinghong Chen State Key Laboratory of Featured Metal Materials and Life‑Cycle Safety for Composite Structures School of ResourcesEnvironment and MaterialsGuangxi UniversityNo.100Daxuedong RoadNanning 530004People’s Republic of China State Key Laboratory of Polymer Materials Engineering Polymer Research Institute of Sichuan UniversitySichuan UniversityNo.24 South Section 1Yihuan RoadChengdu 610065People’s Republic of China

Electromagnetic interference shielding(EMI SE)modules are the core com-ponent of modern ***,the tra-ditional metal-based SE modules always take up indispensable three-dimensional space inside electronics,posing a major obstacle to the integra-tion of *** innovation of integrating 3D-printed conformal shielding(c-SE)modules with packaging materials onto core electronics offers infinite possibilities to satisfy ideal SE func-tion without occupying additional ***,the 3D printable carbon-based inks with various proportions of graphene and carbon nanotube nanoparticles are well-formulated by manipulating their rheological ***,the free-constructed architectures with arbitrarily-customized structure and multifunctionality are created via 3D *** particular,the SE performance of 3D-printed frame is up to 61.4 dB,simultaneously accompanied with an ultralight architecture of 0.076 g cm^(-3) and a superhigh specific shielding of 802.4 dB cm3 g^(-1).Moreover,as a proof-of-concept,the 3D-printed c-SE module is in situ integrated into core electronics,successfully replacing the traditional metal-based module to afford multiple functions for electromagnetic compatibility and thermal ***,this scientific innovation completely makes up the blank for assembling carbon-based c-SE modules and sheds a brilliant light on developing the next generation of high-performance shielding materials with arbitrarily-customized structure for integrated electronics.

关键词： 3D printing Carbon-based nanoparticles Conformal electromagnetic interference shielding Integrated electronics