Geodesic
Modified Galerkin method for the second order equation of mixed type and estimate of its error
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 9 (2016) no. 4, pp. 30-39

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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.
Keywords: equation of mixed type; boundary value problem; approximate solution; Galerkin method; error estimation; regularization. 
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     author = {I. E. Egorov and V. E. Fedorov and I. M. Tikhonova},
     title = {Modified {Galerkin} method for the second order equation of mixed type and estimate of its error},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matemati\v{c}eskoe modelirovanie i programmirovanie},
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I. E. Egorov; V. E. Fedorov; I. M. Tikhonova. Modified Galerkin method for the second order equation of mixed type and estimate of its error. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 9 (2016) no. 4, pp. 30-39. http://geodesic.mathdoc.fr/item/VYURU_2016_9_4_a2/