CONVERGENCE OF SIMPLIFIED AND STABILIZED MIXED ELEMENT FORMATS BASED ON BUBBLE FUNCTION FOR THE STOKES PROBLEM

ＩｎｔｒｏｄｕｃｔｉｏｎＩｎｏｒｄｅｒｔｏｇｅｔｒｉｄｏｆｔｈｅｒｅｓｔｒｉｃｔｉｏｎｔｏｄｉｓｃｒｅｔｅＢａｂｕｓｋａ＿Ｂｒｅｚｚｉ’ｓｃｏｎｄｉｔｉｏｎｓｉｎｒｅｓｅａｒｃｈｅｓｏｆｍｉｘｅｄｆｉｎｉｔｅｅｌｅｍｅｎｔ (ＭＦＥ)ｍｅｔｈｏｄｓ,ｏｎｅｕｓｕａｌｌｙｕｓｅｓｔｈｅｓｔａｂｉｌｉｚｅｄＭＦＥｍｅｔｈｏｄｓｆｏｒｍａｔ[1] .Ｔｈｅｒｅａｒｅａｎｕｍｂｅｒｏｆｓｔａｂｉｌｉｚｅｄｍｅｔｈｏｄｓ (ｓｅｅ ,ｅ.ｇ .,Ｒｅｆｓ.[1- 7]ａｎｄｔｈｅｒｅｆｅｒｅｎｃｅｓｔｈｅｒｅｉｎ) ,ｗｈｉｃｈｈ…     

MIXED FINITE ELEMENT METHODS FOR THE SHALLOW WATER EQUATIONS INCLUDING CURRENT AND SILT SEDIMENTA-TION (Ⅰ)-THE CONTINUOUS-TIME CASE

IntroductionTheshallowwaterequationsareanimportantmathematicalmodelforavarietyofprobleminhydraulicengineering .Inrecentyears,therehasbeeninterestinthenumericalsolutionfortheshallowwaterequations.Thenumericalsimulationsfortheshallowwaterequationsystemcanbeappliedtomanypurposes .First,itcanserveasameansformodelingtidalfluctuationsforthosenterestedincapturingtidalenergyforcommercialpurposes.Secondly ,thesesimulationscanbeusedtocomputetidalrangesandsurgessuchashurricanesandtsunamiscausedbyextreme…     

A Nonlinear Galerkin/Petrov-Least Squares Mixed Element Method for the Stationary Navier-Stokes Equation

A nonlinear Galerkin/ Petrov- least squares mixed element (NGPLSME) method for the stationary Navier-Stokes equations is presented and analyzed. The scheme is that Petrov-least squares forms of residuals are added to the nonlinear Galerkin mixed element method so that it is stable for any combination of discrete velocity and pressure spaces without requiring the Babuska-Brezzi stability condition. The existence, uniqueness and convergence ( at optimal rate ) of the NGPLSME solution is proved in the case of sufficient viscosity ( or small data).     

A NONLINEAR GALERKIN/PETROV-LEAST SQUARES MIXED ELEMENT METHOD FOR THE STATIONARY NAVIER-STOKES EQUATIONS

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｎｏｎｌｉｎｅａｒＧａｌｅｒｋｉｎｍｅｔｈｏｄｉｓａｍｕｌｔｉ＿ｌｅｖｅｌｓｃｈｅｍｅｔｏｆｉｎｄｔｈｅａｐｐｒｏｘｉｍａｔｅｓｏｌｕｔｉｏｎｆｏｒｔｈｅｄｉｓｓｉｐａｔｉｖｅＰＤＥ .ＴｈｉｓｍｅｔｈｏｄｈａｓｆｉｒｓｔｍａｉｎｌｙｂｅｅｎａｄｄｒｅｓｓｅｄｂｙＦｏｉａｓ＿Ｍａｎｌｅｙ＿Ｔｅｍａｍ[1],Ｍａｒｉｏｎ＿Ｔｅｍａｍ[2 ],Ｆｏｉａｓ＿Ｊｏｌｌｙ＿Ｋｅｖｒｅｋｉｄｉｓ＿Ｔｉｔｉ[3]ａｎｄＤｅｖｕｌｄｅｒ＿Ｍａｒｉｏｎ＿Ｔｉｔｉ[4 ]ｉｎｔｈｅｃａｓｅｏｆｓｐｅｃｔ…     

Galerkin-Petrov least squares mixed element method for stationary incompressible magnetohydrodynamics

The Galerkin-Petrov least squares method is combined with the mixed finite element method to deal with the stationary, incompressible magnetohydrodynamics system of equations with viscosity. A Galerkin-Petrov least squares mixed finite element format for the stationary incompressible magnetohydrodynamics equations is presented. And the existence and error estimates of its solution are derived. Through this method, the combination among the mixed finite element spaces does not demand the discrete Babuska-Brezzi stability conditions so that the mixed finite element spaces could be chosen arbitrartily and the error estimates with optimal order could be obtained.     

迈克尔逊干涉仪实验中容易忽视的一个问题

基于迈克尔逊干涉仪相关的光学实验是普通物理实验课程中的重要实验内容。在实验过程中,我们针对观察屏上光点的对齐而无干涉条纹的问题进行研究,分析了出现这一问题的原因并提出了解决办法。     

衍射光栅实验中平行光正入射条件的讨论

针对光栅衍射实验中如何保证平行光正入射光栅表面这一难点,总结出一种在实验教学简单可行、易于学生理解的操作方法。这种实验方法,既包含了分光计调节的基本要求,又能让学生比较容易掌握和理解光栅的衍射理论,提高了实验效率。     

Yb3+,Er3+掺杂的SrAl2O4:Eu2+,Dy3+长余辉材料的发光特性

根据Dorenbos能级模型的推论,利用掺杂Yb3+和Er3+对典型的长余辉材料SrAl2O4:Eu2+,Dy3+(简称SAO:ED)的发光特性(发光强度和余辉时间)进行调制.在发光特性分析中,发展并使用了一种简便易行的解析模型,而不是常用的多项e指数衰减函数的经验模型.研究发现,正如Dorenbos所预言的,Yb+3...     

基于LED的色度学实验研究

作为环保、节能、可智能控制的新型光源,发光二极管（LED）广泛应用于人们的现代生活、生产中,更有望替代传统的照明光源。以三基色LED为光源,制作了三路独立可调恒流电源,通过调节三基色光的不同配比实现加法混色,研究设计了加法混色的色度学实验,既可以直接观察混色后的实验现象,又能通过测量光谱数据得到色度参数。LED光源环保...     

液相色谱-电喷雾串联质谱法测定冬青芽中的脱落酸

建立了测定植物中痕量脱落酸 (ABA) 的液相色谱-电喷雾串联质谱联用分析方法. 植物提取液先采用固相萃取 (SPE) 富集脱落酸并消除基体干扰, 然后以C18柱为固定相, V(甲醇)∶V(2 g/L甲酸水溶液)＝50∶50为流动相分离脱落酸. 电喷雾(ESI)串联质谱采用负离子模式. 选择反应监测 (SRM) 模式用于脱落酸定量, 选择的离子对是263→153, 219. 脱落酸的线性范围为0.005～10 μg/mL, 检测限 (S/N=3) 为0.003 μg/mL, 加标0.02 μg和0.05 μg的回收率分别为98.3% 和103.5%. 该方法用于冬青芽中脱落酸的分析, 结果表明所建立的SPE-LC-MS/MS方法对于分析植物中的痕量脱落酸是有效的.