И.А. Чернов.
Сходимость разностной схемы для модели термодинамики морского льда
// Труды КарНЦ РАН. No 3. Сер. Математическое моделирование и информационные технологии. Вып. 1. 2010. C. 87-92
I.A. Chernov. Convergence of the difference scheme for the model of sea ice thermal dynamics // Transactions of Karelian Research Centre of Russian Academy of Science. No 3. Mathematical Modeling and Information Technologies. 2010. Pp. 87-92
Keywords: thermal dynamics of sea ice, boundary-value problems of heat conduction, the Stefan problem, free boundary, convergence of lattice methods
We consider the locally one-dimensional model of thermal dynamics of sea ice. This is a boundary-value problem of heat conduction with a free boundary and nonlinear boundary condition. For this problem we construct the lattice numerical method and prove that the lattice solution and its lattice derivatives are bounded uniformly with respect to the lattice steps. This implies the convergence of the lattice solution to the weak solution to the boundary-value problem. A difficulty is the Dirichlet boundary condition of the water-ice boundary: we consider a sequence of problems with Neumann conditions with consequent passing to limit.
