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

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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.