【摘 要】
：
In this paper,the unconditional error estimates are presented for the time-dependent Navier-Stokes equations by the bilinear-constant scheme.The corresponding optimal error estimates for the velocity and the pressure are derived unconditionally,while the
【机 构】
：
School of Mathematics,Zhengzhou University of Aeronautics,Zhengzhou 450046,China;School of Mathemati
论文部分内容阅读
In this paper,the unconditional error estimates are presented for the time-dependent Navier-Stokes equations by the bilinear-constant scheme.The corresponding optimal error estimates for the velocity and the pressure are derived unconditionally,while the previous works require certain time-step restrictions.The analysis is based on an iterated time-discrete system,with which the error function is split into a temporal error and a spatial error.The T-independent (T is the time stepsize) error estimate between the numerical solution and the solution of the time-discrete system is proven by a rigorous analysis,which implies that the numerical solution in L∞-norm is bounded.Thus optimal error estimates can be obtained in a traditional way.Numerical results are provided to confirm the theoretical analysis.
其他文献
For an integrator when applied to a highly oscillatory system,the near conservation of the oscillatory energy over long times is an important aspect.In this paper,we study the long-time near conservation of oscillatory energy for the adapted average vecto
近三十年来,美国高中物理教科书的习题设计具有指示性强、设计意图明确、有较好的历史深度与生活宽度等特色.其习题设计变化特点有:习题结构与层次不断优化;习题标准化程度大幅提高;重视科学本质及STEM特色.美国高中物理教科书的习题设计为我国新教科书编制提供了有益启示.
The method of data-driven tight frame has been shown very useful in image restoration problems.We consider in this paper extending this important technique,by incorporating L1 data fidelity into the original data-driven model,for removing impulsive noise
This paper considers adaptive point-wise estimations of density functions in GARCH-type model under the local H(o)lder condition by wavelet methods.A point-wise lower bound estimation of that model is first investigated;then we provide a linear wavelet es
浙科版高中生物学新教材必修1“分子与细胞”模块对实验活动部分进行了调整.从活动编排、插图、讨论、方法步骤4个方面分析其变化,以帮助一线教师更好地理解和发挥新教材实验活动的育人价值.
本文针对2021年河北省普通高中学业水平选择性考试模拟演练第6题螺旋千斤顶问题,从构建等效模型解答题目,到研究学生和老师们热议的系列困惑问题,系统讨论了螺杆螺母、滑块斜面模型中的疑难问题.
肾脏衰老有哪些形态、结构和功能的变化rn衰老是一个自发的渐变过程,使人体产生一系列变化,其中肾脏是易于发生衰老的器官之一.肾脏衰老时外观上会有如下变化:体积缩小,质量减轻,肾皮质萎缩;肾脏表面粗糙化;更多单纯性肾囊肿形成.微观结构上也有改变,包括:动脉硬化,肾小球动脉弯曲缩短,管壁内膜增厚,肾血流量减少;肾小球硬化,肾小管萎缩,肾单位减少;肾脏衰老时“老废物质”蓄积导致肾小管间质纤维化和硬化.
传统课时教学中,生物学事实、概念与观念常常被割裂,使学科核心素养发展受阻.基于单元教学视角,探索事实、概念与观念的融合,促进学生生物学学科核心素养的发展.
大概念的学习需要长期规划与整体设计,即需要在大概念统领下从碎片化的知识点教学走向系统化的单元教学.单元教学需要重构教学内容,帮助学生建立层级式的知识结构,引导学生通过系列具体任务的完成解决指向大概念的基本问题,最后通过真实情境的评价考查学生对大概念的深度理解与迁移应用.这也是落实新课程理念、培育学生生物学学科核心素养的重要路径.
一、教材分析rn“木炭还原氧化铜”为人教版九年级化学上册第六单元课题1“金刚石、石墨和C60”的演示实验6-2.通过实验让学生了解木炭具有还原性,同时为第八单元学习金属的冶炼打下基础.rn教材中实验:把刚烘干的木炭粉末和氧化铜粉末混合均匀,小心地铺放在试管,并固定在铁架台上,试管口装有通入澄清石灰水的导管(见图1),用酒精灯加热.若按课本实验设计进行实验很难看到黑色固体变红的实验现象,而且耗时较长,达不到实验的目的,因此就有教师放弃做该实验.