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Convergence of a numerical scheme for a nonlinear oblique derivative boundary value problem
Published online by Cambridge University Press: 15 January 2003
Abstract
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.
- Type
- Research Article
- Information
- ESAIM: Mathematical Modelling and Numerical Analysis , Volume 36 , Issue 6 , November 2002 , pp. 1111 - 1132
- Copyright
- © EDP Sciences, SMAI, 2002
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