Monotone and second order consistent scheme for the two dimensional Pucci equation
Résumé
We introduce a new strategy for the design of second-order accurate discretizations of non-linear second order operators of Bellman type, which preserves degenerate ellipticity. The approach relies on Selling's formula, a tool from lattice geometry, and is applied to the Pucci equation, discretized on a two dimensional Cartesian grid. Numerical experiments illustrate the robustness and the accuracy of the method.
Note: An earlier version of this document also discussed the Monge-Ampère PDE. This part has been removed in the revised version in order to comply with the page limit of the journal.
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