Modified Galerkin Method for the Second Order Equation of Mixed Type and Estimate of Its Error

Abstract

In this paper, we investigate the boundary value problem for the second order equation of mixed type with an arbitrary manifold of type changing. The theory of such equations 
is based on the applications, in particular, of the transonic gas dynamics. We study equation of elliptic type near the bottom of the cylindrical domain and the hyperbolic or elliptic type near the top of the cylindrical domain. The last case was formulated and studied by authors with another method in the early works. We proved an error estimate for the modified Galerkin method using the regularization parameter and eigenvalues of the Dirichlet problem for the Laplas equation.