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国家自然科学基金(11061021): 作品数：36被引量：64H指数：5; 导出分析报告; 相关作者：刘洋方志朝罗振东季兆义高巍更多>>; 相关机构：内蒙古大学华北电力大学贵州师范大学内蒙古工业大学更多>>; 相关期刊：《理论数学》《高校应用数学学报（A辑）》《高等学校计算数学学报》《Advances in Applied Mathematics and Mechanics》更多>>; 相关主题：最优阶误差估计SOBOLEV方程最优误差估计全离散格式GALERKIN更多>>; 相关领域：理学天文地球航空宇航科学技术更多>>

带有对流项Sobolev方程的基于两个变换的Crank-Nicolson分裂正定混合有限元方法(英文): 《数学进展》2014年第6期869-886,共18页杜艳伟刘洋李宏全明望; Supported by NSFC(No.11301258,No.11361035,No.11061021);Natural Science Fund of Inner Mongolia Autonomous Region(No.2012MS0108,No.2012MS0106);Scientific Research Projection of Higher Schools of Inner Mongolia(No.NJZZ12011,No.NJZY13199);Program of Higher-level Talents of Inner Mongolia University(No.125119); 本文研究和讨论了含对流项二阶Sobolev方程的一个新的分裂正定混合有限元方法.引入两个变换:q=u_t和σ=α(x)▽u+b(x)▽u_t,解关于▽u的常微分方程σ=α(x)▽u+b(x)▽u_t,将Sobolev方程转换成含有三个变量的一阶积分微分系统.在这个积...; 关键词：SOBOLEV方程分裂正定混合有限元方法 CRANK-NICOLSON格式变换误差估计

Fully discrete two-step mixed element method for the symmetric regularized long wave equation被引量：1: 《International Journal of Modeling, Simulation, and Scientific Computing》2014年第3期88-103,共16页Meng Zhao Yang Liu Hong Li; supported by the National Natural Science Fund of China(11061021,11301258 and 11361035);the Scientific Research Projection of Higher Schools of Inner Mongolia(NJZZ12011 and NJZY13199);the Natural Science Fund of Inner Mongolia Province(2012MS0106 and 2012MS0108);the Program of Higher-level talents of Inner Mongolia University(125119).; A numerical method based on the explicit two-step method in time direction and the mixed finite element method in spatial direction is presented for the symmetric regularized long wave(SRLW)equation.The optimal a prio...; 关键词：SRLW equation two-step method mixed finite element method a priori error estimates optimal convergence

A NEW CHARACTERISTIC EXPANDED MIXED METHOD FOR SOBOLEV EQUATION WITH CONVECTION TERM: 《International Journal of Modeling, Simulation, and Scientific Computing》2014年第1期48-67,共20页YANG LIU HONG LI SIRIGULENG HE ZHICHAO FANG JINFENG WANG; supported by the National Natural Science Fund of China(11061021);the Scientific Research Projection of Higher Schools of Inner Mongolia(NJZZ12011,NJZY13199);the Natural Science Fund of Inner Mongolia Province(2012MS0108,2012MS0106);the Program of Higher-level talents of Inner Mongolia University(125119,30105-125132).; In this paper,a new numerical method based on a new expanded mixed scheme and the characteristic method is developed and discussed for Sobolev equation with convection term.The hyperbolic part d(x)∂u/∂t+c(x,t)·∇u is ...; 关键词：Sobolev equation new expanded mixed scheme square integrable(L^(2)(Ω))^(2)space characteristic method a priori error estimates

半线性分数阶扩散方程的时空有限元方法:间断Galerkin方法(英文)被引量：2: 《应用数学》2013年第4期853-862,共10页刘金存李宏; Supported by the National Natural Science Fund (11061021);the National Science Foundation of Inner Mongolia (2012MS0106);the Endancing Comprehensive Strength Project of Inner Mongolia University (14020202); 本文研究半线性分数阶扩散问题的Galerkin时空有限元方法,该方法在空间连续,而在时间上间断.将有限元与有限差分方法相结合,充分利用拉格朗日插值多项式在Radau点处的特性,给出弱解的存在唯一性证明,且不需对时空网格施加任何限制.通过...; 关键词：分数阶扩散方程间断GALERKIN方法存在唯一性误差估计

Sobolev方程的一类新型H^1-Galerkin混合元法被引量：1: 《高等学校计算数学学报》2013年第3期206-221,共16页李宏季兆义刘洋何斯日古愣; 国家自然科学基金(11061021);内蒙古自治区高等学校科学研究项目(NJZZ12011,NJZY13199);内蒙古自然科学基金(2012MS0106,2012MS0108);内蒙古大学高层次人才基金(125119,30105-125132); 考虑如下半线性Sobolev方程的初边值问题：; 关键词：数学数学分析粘弹性方程二阶非协调有限元逼近分析

阻尼Sine-Gordon方程基于三角网格剖分的混合控制体积方法（英文）被引量：2: 《数学进展》2013年第4期441-457,共17页方志朝李宏; Supported by NSFC(No.11061021);the Science Research of Inner Mongolia Advanced Education(No.NJ10016,No.NJZZ12011);the National Science Foundation of Inner Mongolia Province(No.2011BS0102,No.2012MS0106); 本文利用混合控制体积方法在三角网格剖分下求解阻尼Sine-Gordon方程.通过使用最低阶Raviart-Thomas混合有限元空间和引入迁移算子把解函数空间映射成试探函数空间,构造了半离散和全离散的混合控制体积格式.根据阻尼Sine-Gordon方程的...; 关键词：阻尼Sine-Gordon方程混合控制体积方法全离散格式最优阶误差估计

Time discontinuous Galerkin space-time finite element method for nonlinear Sobolev equations: 《Frontiers of Mathematics in China》2013年第4期825-836,共12页Siriguleng HE Hong LI Yang LIU; This work was supported in part by the National Natural Science Foundation of China （Grant No. 11061021）, Natural Science Fund of Inner Mongolia Autonomous Region （2012MS0106, 2012MS0108）, Scientific Research Projection of Higher Schools of Inner Mongolia （NJZZ12011, N J10006, NJZY13199）, and the Program of Higherlevel talents of Inner Mongolia University （125119, 30105-125132）.; This article presents a complete discretization of a nonlinear Sobolev equation using space-time discontinuous Galerkin method that is discontinuous in time and continuous in space. The scheme is formulated by introdu...; 关键词：Nonlinear Sobolev equation time finite element method optimal error time discontinuous Galerkin spaceestimate

Numerical solutions to regularized long wave equation based on mixed covolume method被引量：3: 《Applied Mathematics and Mechanics(English Edition)》2013年第7期907-920,共14页方志朝李宏; supported by the National Natural Science Fundation of China (No. 11061021);the Science Research of Inner Mongolia Advanced Education (Nos. NJ10006, NJ10016, and NJZZ12011);the National Science Foundation of Inner Mongolia (Nos. 2011BS0102 and 2012MS0106); The mixed covolume method for the regularized long wave equation is devel- oped and studied. By introducing a transfer operator γh, which maps the trial function space into the test function space, and combining the ...; 关键词：regularized long wave equation mixed covolume method fully discrete optimal error estimate

伪双曲型方程的混合控制体积方法被引量：2: 《数学物理学报（A辑）》2013年第3期535-550,共16页方志朝李宏罗振东; 国家自然科学基金(11061021,11061009);内蒙古高校科学研究项目(NJ10006)资助; 利用混合控制体积方法在三角形网格剖分下求解一类伪双曲型方程.通过使用最低阶Raviart-Thomas混合有限元空间和引入迁移算子把解函数空间映射成试探函数空间,构造了半离散和全离散的混合控制体积格式.根据伪双曲型方程的特点引入广义...; 关键词：伪双曲型方程混合控制体积方法全离散格式最优阶误差估计

A new mixed scheme based on variation of constants for Sobolev equation with nonlinear convection term被引量：1: 《Applied Mathematics(A Journal of Chinese Universities)》2013年第2期158-172,共15页LIU Yang LI Hong HE Siriguleng GAO Wei MU Sen; Supported by National Natural Science Fund of China (11061021);Key Project of Chinese Ministry of Education (12024);Natural Science Fund of Inner Mongolia Autonomous Region (2012MS0108,2012MS0106,2011BS0102);Scientific Research Projection of Higher Schools of Inner Mongolia (NJZZ12011,NJZY13199);Program of Higher-level talents of Inner Mongolia University (125119,Z200901004,30105-125132); A new mixed scheme which combines the variation of constants and the H1-Galerkin mixed finite element method is constructed for nonlinear Sobolev equation with nonlinear con- vection term. Optimal error estimates are ...; 关键词：Sobolev equation NONLINEAR convection term variation of constants H1-Galerkin mixed method optimal error estimate.

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