CONVERGENCE_ANALYSIS

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Unconditional Superconvergence Analysis of Energy Conserving Finite Element Methods for the Nonlinear Coupled Klein-Gordon Equations
《Advances in Applied Mathematics and Mechanics》2023年第3期602-622,共21页Ming Cui Yanfei Li Changhui Yao 
The work is supported by the National Natural Science Foundation of China(No.11871441);Beijing Natural Science Foundation(No.1192003).
In this paper,we consider the energy conserving numerical scheme for coupled nonlinear Klein-Gordon equations.We propose energy conserving finite element method and get the unconditional superconvergence resultO(h^(2)...
关键词：Energy conserving the nonlinear coupled Klein-Gordon equations unconditional superconvergence result postprocessing interpolation finite element method 
A New Framework of Convergence Analysis for Solving the General Nonlinear Schrodinger Equation using the Fourier Pseudo-Spectral Method in Two Dimensions
《Advances in Applied Mathematics and Mechanics》2023年第3期786-813,共28页Jialing Wang Tingchun Wang Yushun Wang 
Jialing Wang’s work is supported by the National Natural Science Foundation of China(Grant No.11801277);Tingchun Wang’s work is supported by the National Natural Science Foundation of China(Grant No.11571181);the Natural Science Foundation of Jiangsu Province(Grant No.BK20171454);Qing Lan Project.Yushun Wang’s work is supported by the National Natural Science Foundation of China(Grant Nos.11771213 and 12171245).
This paper aims to build a new framework of convergence analysis of conservative Fourier pseudo-spectral method for the general nonlinear Schr¨odinger equation in two dimensions,which is not restricted that the nonli...
关键词：Framework of convergence analysis general nonlinear Schr¨odinger equation Fourier pseudo-spectral method conservation laws unconditional convergence blow-up solution 
AConservative Upwind Approximation on Block-Centered Difference for Chemical Oil Recovery Displacement Problem
《Advances in Applied Mathematics and Mechanics》2022年第6期1246-1275,共30页Changfeng Li Yirang Yuan Aijie Cheng Huailing Song 
the Natural Science Foundation of Shandong Province(Grant No.ZR2021MA019);Natural Science Foundation of Hunan Province(Grant No.2018JJ2028);National Natural Science Foundation of China(Grant No.11871312).
A kind of conservative upwind method is discussed for chemical oil recovery displacement in porous media.The mathematical model is formulated by a nonlinear convection-diffusion system dependent on the pressure,Darcy ...
关键词：Chemical oil recovery upwind block-centered difference fractional step difference elemental conservation convergence analysis. 
Convergence Analysis and Error Estimate for Distributed Optimal Control Problems Governed by Stokes Equations with Velocity-Constraint被引量：1
《Advances in Applied Mathematics and Mechanics》2022年第1期33-55,共23页Liang Ge Haifeng Niu Jianwei Zhou 
supported by NSFC grants(Nos.11926355,and 11701253);NSF of Henan Province(No.15A110024);NSF of Shandong Province(Nos.ZR2019YQ05,2019KJI003,and 2017GSF216001);China Postdoctoral Science Foundation(Nos.2017T100030,and 2017M610751)。
In this paper,spectral approximations for distributed optimal control problems governed by the Stokes equation are considered.And the constraint set on velocity is stated with L2-norm.Optimality conditions of the cont...
关键词：Optimal control spectral approximation Stokes equation convergence analysis 
Error Estimate of a Second Order Accurate Scalar Auxiliary Variable (SAV) Numerical Method for the Epitaxial Thin Film Equation被引量：3
《Advances in Applied Mathematics and Mechanics》2021年第6期1318-1354,共37页Qing Cheng Cheng Wang 
supported in part by NSF DMS-2012669(C.Wang).
A second order accurate(in time)numerical scheme is analyzed for the slope-selection(SS)equation of the epitaxial thin film growth model,with Fourier pseudo-spectral discretization in space.To make the numerical schem...
关键词：Epitaxial thin film equation Fourier pseudo-spectral approximation the scalar auxiliary variable(SAV)method Crank-Nicolson temporal discretization energy stability optimal rate convergence analysis. 
A New Mixed Finite Element Method for Biot Consolidation Equations被引量：1
《Advances in Applied Mathematics and Mechanics》2020年第6期1520-1541,共22页Luoping Chen Yan Yang 
supported by the National Natural Science Foundation of China under Grant Nos.11501473,11426189 and the Fundamental Research Funds for the Central Universities of China(No.2682016CX108).
In this paper,we study a new finite element method for poroelasticity problem with homogeneous boundary conditions.The finite element discretization method is based on a three-variable weak form with mixed finite elem...
关键词：Biot consolidation equations linear elasticity finite element method convergence analysis. 
Convergence Analysis on Stochastic Collocation Methods for the Linear Schr¨odinger Equation with Random Inputs被引量：1
《Advances in Applied Mathematics and Mechanics》2020年第1期30-56,共27页Zhizhang Wu Zhongyi Huang 
supported by the National Key Research and Development Plan of China No.2017YFC0601801 and NSFC Project No.11871298.
In this paper,we analyse the stochastic collocation method for a linear Schr¨odinger equation with random inputs,where the randomness appears in the potential and initial data and is assumed to be dependent on a rand...
关键词：Schrodinger equation stochastic collocation methods convergence analysis uncertainty quantification 
Superconvergence Analysis for the Maxwell’s Equations in Debye Medium with a Thermal Effect
《Advances in Applied Mathematics and Mechanics》2020年第1期141-163,共23页Changhui Yao Dongyang Shi Mengmeng Hou 
supported by NSFC(Nos.11871441 and 11571389)and the Specialized Research Fund for State Key Laboratory of Space Weather(No.201916);The second author is supported by NSFC(No.11671369).
In this paper,a mixed finite element method is investigated for the Maxwell’s equations in Debye medium with a thermal effect.In particular,in two dimensional case,the zero order N´ed´elec element(Q01Q10),the piec...
关键词：Maxwell’s equations thermal effect error analysis SUPERCONVERGENCE 
Convergence Analysis for the Chebyshev Collocation Methods to Volterra Integral Equations with a Weakly Singular Kernel被引量：2
《Advances in Applied Mathematics and Mechanics》2017年第6期1506-1524,共19页Xiong Liu Yanping Chen 
The authorswould like to thank the referees for the helpful suggestions.Thiswork is supported by National Science Foundation of China(Nos.91430104,11671157 and 11401347);Lingnan Normal University Project(No.2014YL1408)。
In this paper,a Chebyshev-collocation spectral method is developed for Volterra integral equations(VIEs)of second kind with weakly singular kernel.We first change the equation into an equivalent VIE so that the soluti...
关键词：Chebyshev collocation method Volterra integral equations spectral rate of convergence H¨older continuity 
Convergence Analysis of Legendre-Collocation Methods for Nonlinear Volterra Type Integro Equations被引量：1
《Advances in Applied Mathematics and Mechanics》2015年第1期74-88,共15页Yin Yang Yanping Chen Yunqing Huang Wei Yang 
supported by National Science Foundation of China(11301446,11271145);Foundation for Talent Introduction of Guangdong Provincial University,Specialized Research Fund for the Doctoral Program of Higher Education(20114407110009);the Project of Department of Education of Guangdong Province(2012KJCX0036);China Postdoctoral Science FoundationGrant(2013M531789);Project of Scientific Research Fund ofHunan Provincial Science and Technology Department(2013RS4057);the Research Foundation of Hunan Provincial Education Department(13B116).
A Legendre-collocation method is proposed to solve the nonlinear Volterra integral equations of the second kind.We provide a rigorous error analysis for the proposed method,which indicate that the numerical errors in ...
关键词：Spectral method NONLINEAR Volterra integral equations 
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