On a precision estimate for a hydrodynamics problem with discontinuous coefficients in the norm of the space $\mathbf L_2(\Omega_h)$

We study the 2-dimensional problem obtained by time-discretizing and linearizing the problem of flow of a 2-phase viscous fluid without mixing in the statement of incompressible Navier–Stokes equations with time-dependent interface. For an approximate solution to this problem we construct a scheme of a nonconformal finite element method. We estimate the rate of convergence of the mesh solution to the exact solution to the problem in the norm of $\mathbf L_2(\Omega_h)$, which agrees with simulations.