Incremental Unknowns Method for Solving Three-Dimensional Convection-Diffusion Equations

We use the incremental unknowns method in conjunction with the iterative methods to approximate the solution of the nonsymmetric and positive-definite linear systems generated from a multilevel discretization of three-dimensional convection-diffusion equations. The condition numbers of incremental unknowns matrices associated with the convection-diffusion equations and the number of iterations needed to attain an acceptable accuracy are estimated. Numerical results are presented with two-level approximations, which demonstrate that the incremental unknowns method when combined with some iter- ative methods is very effcient.     

压力项属于Triebel-Lizorkin空间的三维不可压Navier-Stokes方程的正则性准则

该文研究了R³中的Navier-Stokes方程弱解的正则性准则,证明了当π∈L^p(0,T;■(R³))时Leray-Hopf弱解u是正则的,其中2/p+3/q<7/4,12/5p(0,T;■(R³)),弱解u能光滑的延拓出t=T,其中2/p+3/q=11/4,12/11相似文献   

Navier-Stokes-Coriolis方程解的长时间存在性

该文应用Littlewood-Paley分解, Strichartz估计及高低频分解方法研究了不可压缩Navier-Stokes-Coriolis方程在Sobolev空间H^s(s> 4)中解长时间存在性.     

在传承与发展中加强化学基础实验课程体系建设

实验教学在化学学科人才培养体系中发挥着重要作用,吉林大学化学学科已历70年的发展,在传承“厚基础、强能力、重实践”的教学传统的同时,顺应时代发展,构建了新的“两阶段、三层次”的基础实验教学体系,融入新的教学内容。在先进的育人理念指导下,构建了满足个性化和差异化教学的多层次基础实验课程体系,全方位提升学生实验能力和综合素养。     

NODAL O（h^4）-SUPERCONVERGENCE IN 3D BY AVERAGING PIECEWISE LINEAR,BILINEAR, AND TRILINEAR FE APPROXIMATIONS

We construct and analyse a nodal O（h^4）-superconvergent FE scheme for approximating the Poisson equation with homogeneous boundary conditions in three-dimensional domains by means of piecewise trilinear functions. The scheme is based on averaging the equations that arise from FE approximations on uniform cubic, tetrahedral, and prismatic partitions. This approach presents a three-dimensional generalization of a two-dimensional averaging of linear and bilinear elements which also exhibits nodal O（h^4）-superconvergence （ultracon- vergence）. The obtained superconvergence result is illustrated by two numerical examples.     

一个描述Josephson振动阻尼效应的场方程

在GPE方程的基础上添加了一个耗散项-12γcψ,用来分析双势阱模型的Josephson振荡中的阻尼现象,并得出:凝聚态粒子总数及 Josephson振动的振幅随时间呈指数衰减.     

盘声珠韵——图说中国算盘发展简史

<正>五、通商惠工——清代民国时期算盘的普及清代珠算广泛使用。上至天文历算,下至农田水利;大到国家经济发展,小到百姓家庭生活,都离不开算盘。珠算在促进经济发展、推动社会进步方面,发挥了极为重要的作用。民国时期,新工业兴办,     

半线性抛物方程的时空有限元方法的误差估计

<正>1引言本文考虑如下半线性抛物方程(?)其中Ω∈R~2.函数f(u):C→C满足:(1)|f(u)|≤c|u|(?)u∈C(Ω)(2)Lipschitz条件,即     

求解二维Poisson方程的重心插值配点法

采用重心Lagrange插值配点法计算了二维Poisson方程.采用重心Lagrange插值法构造近似函数,由配点法离散Poisson方程及其边界条件.数值算例表明方法具有理论简单、计算精度高的特点.     

一般的高阶线性差分方程的求解研究

本文首先研究了k阶线性差分方程的解的结构,其次给出了齐次方程的基础解系的判定方法和存在条件,并得到相应齐次差分方程通解的具体表达式,最后用实例进行了验证.