About convergence speed of the stationary Galerkin method for the mixed type equation

In this paper it is investigated the boundary value problem of V.N. Vragov for mixed-type equation of second order, when equation belongs to elliptic type close to the cylindrical base region. Using a stationary Galerkin methods we prove the unique regular solvability of this boundary value problem. It was established a priori estimates for mixed-type equation. It is obtained an estimate for the rate convergence of Galerkin method in the steady-state rate of the Sobolev spaces by eigenfunctions of the Laplace operator in the spatial variables and time. For derivation of the estimate of convergence of stationary Galerkin methods we use the expantion of solution of the initial boundary value problem.