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…     

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.     

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…     

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…     

定常的热传导-对流问题的Galerkin/Petrov最小二乘混合元方法

1.引言 热传导-对流问题是大气动力学中的一个重要的方程,这个方程组也称为强迫耗散的非线性系统方程组,其较Navier-Stokes方程多了一个未知函数温度场,且温度与速度和压力之间存在着复杂的非线性关系.从热动力学可知,任何运动都会产生热量即有温度,而且温度与速度和压力之间必定互相转化,因此对该非线性系统的研究更具有实际意义.[1]先对     

定常的磁流体动力学问题的Galerkin/Petrov最小二乘混合元方法

提出了定常的磁流体动力学方程的一种Galerkin-Petrov最小二乘混合元法,并导出Galerkin-Petrov最小二乘混合元解的存在性和误差估计.通过引入Galerkin-Petrov最小二乘混合有限元方法使得该方法的混合元空间之间的组合无需满足离散的Babuska-Brezzi稳定性条件,从而使得它们的混合有限元空间可以任意选取,并得到误差估计最优阶.     

非定常的热传导-对流问题的非线性Galerkin混合元法(Ⅲ):时间二阶精度的全离散格式

In this paper, a fully discrete format of nonlinear Galerkin mixed element method with two-step discretization of time for the non stationary conduction-convection problems is presented. The existence and the convergence of the fully discrete mixed element solution are shown. On the basis of [9] and [10], we have proved that the schemes have second-order convergence accuracy for the time discretization.