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Monotone and second order consistent scheme for the two dimensional Pucci equation

Abstract : 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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https://hal.archives-ouvertes.fr/hal-02383521
Contributor : Jean-Marie Mirebeau Connect in order to contact the contributor
Submitted on : Sunday, May 31, 2020 - 9:58:36 PM
Last modification on : Wednesday, April 20, 2022 - 3:44:05 AM

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Joseph Frédéric Bonnans, Guillaume Bonnet, Jean-Marie Mirebeau. Monotone and second order consistent scheme for the two dimensional Pucci equation. Numerical Mathematics and Advanced Applications ENUMATH 2019., Sep 2019, Egmond aan Zee, Netherlands. pp 733-742, ⟨10.1007/978-3-030-55874-1_72⟩. ⟨hal-02383521v2⟩

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