The stationary Galerkin method for a boundary value problem for a mixed second-order equation

We prove the existence of the unique regular solution for the boundary value problem for the mixed type second-order equation in the Sobolev space. The stationary Galerkin method is applied, for which the error estimate is obtained using eigenvalues of the spectral problem for the Laplace equation in the variables $x\in R^n$ and $t$.