Geodesic
Galerkin's method for equations with a small parameter in the highest order derivatives
Sbornik. Mathematics, Tome 14 (1971) no. 4, pp. 525-536 
L. A. Kalyakin. Galerkin's method for equations with a small parameter in the highest order derivatives. Sbornik. Mathematics, Tome 14 (1971) no. 4, pp. 525-536. http://geodesic.mathdoc.fr/item/SM_1971_14_4_a3/
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Voir la notice de l'article provenant de la source Math-Net.Ru

The question considered is the convergence of Galerkin's method for the operator equation $A_\varepsilon u-Ku\equiv\varepsilon A_1u+A_0u-Ku=f$, where $A_0$ is positive definite, $A_1$ is positive semidefinite with domain of definition $D(A_1)\subset D(A_0)$, and $\varepsilon>0$ is a small parameter. With certain additional natural assumptions it is shown that the solution obtained by Galerkin's method is uniformly convergent to the true solution in the norm defined by the quadratic form $(A_\varepsilon u,u)$ for $0\leqslant\varepsilon\leqslant1$. Bibliography: 7 titles.

[1] S. G. Mikhlin, Variatsionnye metody v matematicheskoi fizike, Gostekhizdat, Moskva–Leningrad, 1957

[2] N. I. Polskii, “O skhodimosti nekotorykh priblizhennykh metodov analiza”, Ukr. matem. zh., 7:1 (1956), 56–70 | MR

[3] M. I. Vishik, “Zadacha Koshi dlya uravnenii s operatornymi koeffitsientami, smeshannaya kraevaya zadacha dlya sistem differentsialnykh uravnenii i priblizhennyi metod ikh resheniya”, Matem. sb., 39(81) (1956), 51–148

[4] K. Moren, Metody gilbertova prostranstva, Mir, Moskva, 1965 | MR

[5] M. Sh. Birman, “Metody kvadratichnykh form v zadachakh o malom parametre pri starshikh proizvodnykh”, Vestnik LGU, 13:3 (1957), 9–12 | MR | Zbl

[6] L. A. Kalyakin, “Metod Rittsa dlya uravnenii s malym parametrom pri starshikh proizvodnykh”, Matem. zametki, 6:1 (1969), 91–96

[7] N. Danford, Dzh. T. Shvarts, Lineinye operatory. Obschaya teoriya, IL, Moskva, 1962