Convergence Speed of the Stationary Galerkin Method for the Mixed Type Equation

The paper studies the boundary value problem of V.N. Vragov for mixed-type equation of the second order, when equation belongs to elliptic type which is close to the cylindrical base region. Using a stationary Galerkin method we prove the unique regular solvability of this boundary value problem. Priori estimates are given for mixed-type equations. An estimate for the rate convergence of Galerkin method in the steady-state rate of the Sobolev spaces is obtained 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 expansion of solution of the initial boundary value problem.

Keywords

equation of mixed type, stationary, the Galerkin method, boundary value problem, unequality, estimate

References

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