Difference melt model

The basic objective of the research is to construct a difference model of the melt motion. The existence of a solution to the problem is proven in the paper. It is also proven the convergence of the difference problem solution to the original problem solution of the melt motion. The Rothe method is implemented to study the Navier-Stokes equations, which provides the study of the boundary value problems correctness for a viscous incompressible flow both numerically and analytically.