High accuracy finite element method for flow problem with moving boundary and relative topics

本文研究了不可压缩双流体流动的无通量有限元方法，并对不连续黏度和密度情况下广义Stokes界面问题的无通量有限元方法的质量守恒、误差估计和近似解的收敛性进行了数学考虑。Okumura采用SLG特征有限元法考虑自由界面流动问题，采用Hermite元，采用CSF法考虑表面张力效应。Murakawa处理了一个带有三结点的移动边界问题。他提供了这个问题的一个弱公式，它隐含地包含了移动边界的信息。此外，他还提出并分析了一种捕获运动边界的有效数值方法。Yamaguchi利用解析半群理论证明了惩罚型Navier-Stokes方程的Cauchy问题的心解在惩罚参数趋于零时收敛于原问题的心解。

In this research we considered the flux-free finite element method for incompressible two-fluid flows and we gave the mathematical considerlation for the mass conservation, error estimates and the convergence of the approximate solution of the flux-free finite element method for the genelarized Stokes interface problem in the case of discontinuous viscosity and density.Okumura considered the free-interface flow problem using the SLG characteristic finite element method with the Hermite element and the surface tension effect by the CSF method. Murakawa treated a moving boundary problem with triple-junction points. He provided a weak formulation of the problem which implicitly involves the information of the moving boundaries. Moreover, he proposed and analyzed an efficient numerical method for caputuring the moving boundaries. Yamaguchi had by analytic semigroup theory that mind solution of the Cauchy problem of penalized Navier-Stokes equations converges to that of original problem when penalty parameter tends to zero.