Convergence of a numerical scheme for a nonlinear oblique derivative boundary value problem
MIP, UMR CNRS 5640, Université Paul Sabatier, 118, route de Narbonne,
31062 Toulouse Cedex 04, France. firstname.lastname@example.org.
Revised: 23 July 2002
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.
Mathematics Subject Classification: 35K60 / 65N12
Key words: Oblique derivative boundary problem / finite difference scheme / heat equation / Burgers equation.
© EDP Sciences, SMAI, 2002