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

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. 
@article{SM_1971_14_4_a3,
     author = {L. A. Kalyakin},
     title = {Galerkin's method for equations with a~small parameter in the highest order derivatives},
     journal = {Sbornik. Mathematics},
     pages = {525--536},
     publisher = {mathdoc},
     volume = {14},
     number = {4},
     year = {1971},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1971_14_4_a3/}
}
TY  - JOUR
AU  - L. A. Kalyakin
TI  - Galerkin's method for equations with a~small parameter in the highest order derivatives
JO  - Sbornik. Mathematics
PY  - 1971
SP  - 525
EP  - 536
VL  - 14
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SM_1971_14_4_a3/
LA  - en
ID  - SM_1971_14_4_a3
ER  - 
%0 Journal Article
%A L. A. Kalyakin
%T Galerkin's method for equations with a~small parameter in the highest order derivatives
%J Sbornik. Mathematics
%D 1971
%P 525-536
%V 14
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SM_1971_14_4_a3/
%G en
%F SM_1971_14_4_a3
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/