The stationary Galerkin method applied to the first boundary value problem for a higher order equation with changing time direction

We prove the existence of the unique regular solution to the first boundary value problem for the higher order equation with changing time direction in the Sobolev space. The stationary Galerkin method is applied for which the estimate of the rate of convergence is obtained in the terms of the eigenvalues to the self-adjoint spectral problem for the quasielliptic equation.