Geodesic
The stationary Galerkin method for a boundary value problem for a mixed second-order equation
Matematičeskie zametki SVFU, Tome 23 (2016), pp. 82-90

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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 $t$.
Keywords: mixed type equation, boundary value problem, a priori estimate, stationary Galerkin method, error. 
@article{SVFU_2016_23_a6,
     author = {V. E. Fedorov and I. M. Tikhonova},
     title = {The stationary {Galerkin} method for a boundary value problem for a mixed second-order equation},
     journal = {Matemati\v{c}eskie zametki SVFU},
     pages = {82--90},
     publisher = {mathdoc},
     volume = {23},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SVFU_2016_23_a6/}
}
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V. E. Fedorov; I. M. Tikhonova. The stationary Galerkin method for a boundary value problem for a mixed second-order equation. Matematičeskie zametki SVFU, Tome 23 (2016), pp. 82-90. http://geodesic.mathdoc.fr/item/SVFU_2016_23_a6/