We extend the theory of Barles Jakobsen to develop numerical schemes for
Hamilton Jacobi Bellman equations. We show that the monotonicity of the schemes
can be relaxed still leading to the convergence to the viscosity solution of
the equation. We give some examples of such numerical schemes and show that the
bounds obtained by the framework developed are not tight. At last we test some
numerical schemes.Comment: 24 page

Warin, Xavier

ESAIM Proceedings and Surveys

English

arXiv

We extend the theory of Barles Jakobsen [3] for a class of almost monotone schemes to solve stationary Hamilton Jacobi Bellman equations. We show that the monotonicity of the schemes can be relaxed still leading to the convergence to the viscosity solution of the equation even if the discrete problem can only be solved with some error. We give some examples of such numerical schemes and show that the bounds obtained by the framework developed are not tight. At last we test the schemes

Some non monotone schemes for Hamilton-Jacobi-Bellman equations

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