Consistent convergence rate estimates in the grid $W_{2,0}^2(\omega)$ norm for difference schemes approximating nonlinear elliptic equations with mixed derivatives and solutions from $W_{2,0}^m(\Omega)$, $3$
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 57 (2017) no. 9, pp. 1444-1470
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The Dirichlet boundary value problem for nonlinear elliptic equations with mixed derivatives and unbounded nonlinearity is considered. A difference scheme for solving this class of problems and an implementing iterative process are constructed and investigated. The convergence of the iterative process is rigorously analyzed. This process is used to prove the existence and uniqueness of a solution to the nonlinear difference scheme approximating the original differential problem. Consistent with the smoothness of the desired solution, convergence rate estimates in the discrete norm of $W_{2,0}^2(\omega)$ for difference schemes approximating the nonlinear equation with unbounded nonlinearity are established.
@article{ZVMMF_2017_57_9_a3,
author = {F. V. Lubyshev and M. E. Fairuzov},
title = {Consistent convergence rate estimates in the grid $W_{2,0}^2(\omega)$ norm for difference schemes approximating nonlinear elliptic equations with mixed derivatives and solutions from $W_{2,0}^m(\Omega)$, $3<m\leqslant4$},
journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
pages = {1444--1470},
publisher = {mathdoc},
volume = {57},
number = {9},
year = {2017},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_9_a3/}
}
TY - JOUR
AU - F. V. Lubyshev
AU - M. E. Fairuzov
TI - Consistent convergence rate estimates in the grid $W_{2,0}^2(\omega)$ norm for difference schemes approximating nonlinear elliptic equations with mixed derivatives and solutions from $W_{2,0}^m(\Omega)$, $3
JO - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY - 2017
SP - 1444
EP - 1470
VL - 57
IS - 9
PB - mathdoc
UR - http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_9_a3/
LA - ru
ID - ZVMMF_2017_57_9_a3
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%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
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%F ZVMMF_2017_57_9_a3
F. V. Lubyshev; M. E. Fairuzov. Consistent convergence rate estimates in the grid $W_{2,0}^2(\omega)$ norm for difference schemes approximating nonlinear elliptic equations with mixed derivatives and solutions from $W_{2,0}^m(\Omega)$, $3