Convergence of a numerical scheme for a nonlinear oblique derivative boundary value problem
Mehats, Florian
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 36 (2002), p. 1111-1132 / Harvested from Numdam
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We present here a discretization of a nonlinear oblique derivative boundary value problem for the heat equation in dimension two. This finite difference scheme takes advantages of the structure of the boundary condition, which can be reinterpreted as a Burgers equation in the space variables. This enables to obtain an energy estimate and to prove the convergence of the scheme. We also provide some numerical simulations of this problem and a numerical study of the stability of the scheme, which appears to be in good agreement with the theory.

Publié le : 2002-01-01
DOI : https://doi.org/10.1051/m2an:2003008
Classification:  35K60,  65N12 
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     author = {Mehats, Florian},
     title = {Convergence of a numerical scheme for a nonlinear oblique derivative boundary value problem},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     volume = {36},
     year = {2002},
     pages = {1111-1132},
     doi = {10.1051/m2an:2003008},
     mrnumber = {1958661},
     zbl = {1060.65100},
     language = {en},
     url = {http://dml.mathdoc.fr/item/M2AN_2002__36_6_1111_0}
}

Mehats, Florian. Convergence of a numerical scheme for a nonlinear oblique derivative boundary value problem. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 36 (2002) pp. 1111-1132. doi : 10.1051/m2an:2003008. http://gdmltest.u-ga.fr/item/M2AN_2002__36_6_1111_0/

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