Study on the finite element scheme for fluid flows with free interface

On the other hand, as the mathematical analysis of the finite element scheme for two-fluid flows we have considered the convergence of the approximate interface. In fact, estimating the LィイD1pィエD1(Ω)-norm of difference between the measure of positive value of the pseudo-density function and its approximation under the convergence of the finite element solution, we have prove it. Here we have used the Heaviside operator. The mathematical analysis of the total finite element scheme, however, is our theme in the near future.