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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

Florian Mehats
Florian Mehats*
Affiliation:
MIP, UMR CNRS 5640, Université Paul Sabatier, 118, route de Narbonne, 31062 Toulouse Cedex 04, France. mehats@mip.ups-tlse.fr.
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Abstract

We present here a discretization of a nonlinear obliquederivative boundary value problem for the heat equation in dimensiontwo. This finite difference scheme takes advantages of thestructure of the boundary condition, which can be reinterpreted as aBurgers equation in the space variables. This enables to obtain anenergy estimate and to prove the convergence of the scheme. We also provide some numerical simulations of thisproblem and a numerical study of the stability of the scheme, whichappears to be in good agreement with the theory.

Keywords

Oblique derivative boundary problemfinite difference schemeheat equationBurgers equation.
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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References

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