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.
Keywords: oblique derivative boundary problem, finite difference scheme, heat equation, Burgers equation
@article{M2AN_2002__36_6_1111_0, author = {Mehats, Florian}, title = {Convergence of a numerical scheme for a nonlinear oblique derivative boundary value problem}, journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique}, pages = {1111--1132}, publisher = {EDP-Sciences}, volume = {36}, number = {6}, year = {2002}, doi = {10.1051/m2an:2003008}, mrnumber = {1958661}, zbl = {1060.65100}, language = {en}, url = {http://www.numdam.org/articles/10.1051/m2an:2003008/} }
TY - JOUR AU - Mehats, Florian TI - Convergence of a numerical scheme for a nonlinear oblique derivative boundary value problem JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2002 SP - 1111 EP - 1132 VL - 36 IS - 6 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an:2003008/ DO - 10.1051/m2an:2003008 LA - en ID - M2AN_2002__36_6_1111_0 ER -
%0 Journal Article %A Mehats, Florian %T Convergence of a numerical scheme for a nonlinear oblique derivative boundary value problem %J ESAIM: Modélisation mathématique et analyse numérique %D 2002 %P 1111-1132 %V 36 %N 6 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an:2003008/ %R 10.1051/m2an:2003008 %G en %F M2AN_2002__36_6_1111_0
Mehats, Florian. Convergence of a numerical scheme for a nonlinear oblique derivative boundary value problem. ESAIM: Modélisation mathématique et analyse numérique, Volume 36 (2002) no. 6, pp. 1111-1132. doi : 10.1051/m2an:2003008. http://www.numdam.org/articles/10.1051/m2an:2003008/
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