Geodesic
On convergence of the explicit difference scheme for evolution variational inequality with nonlocal space operator
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 157 (2015) no. 4, pp. 5-23

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Nonlinear parabolic variational inequality with a nonlocal space operator monotone with respect to the gradient is considered. Using the methods of penalty and summatory identities, explicit difference scheme with respect to the space operator and implicit difference scheme with respect to the penalty operator are constructed. Conditions of stability for the constructed difference scheme are obtained. The theorem of convergence is proved under minimal assumptions on the smoothness of the original data.
Keywords: variational inequality, operator monotone with respect to gradient, nonlocal operator, explicit difference scheme with penalty operator, stability
Mots-clés : convergence. 
@article{UZKU_2015_157_4_a0,
     author = {O. V. Glazyrina and M. F. Pavlova},
     title = {On convergence of the explicit difference scheme for evolution variational inequality with nonlocal space operator},
     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
     pages = {5--23},
     publisher = {mathdoc},
     volume = {157},
     number = {4},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/UZKU_2015_157_4_a0/}
}
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O. V. Glazyrina; M. F. Pavlova. On convergence of the explicit difference scheme for evolution variational inequality with nonlocal space operator. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 157 (2015) no. 4, pp. 5-23. http://geodesic.mathdoc.fr/item/UZKU_2015_157_4_a0/