AN EFFICIENT FILTERED SCHEME FOR SOME FIRST ORDER HAMILTON-JACOBI-BELLMAN EQUATIONSReport as inadecuate




AN EFFICIENT FILTERED SCHEME FOR SOME FIRST ORDER HAMILTON-JACOBI-BELLMAN EQUATIONS - Download this document for free, or read online. Document in PDF available to download.

1 LJLL - Laboratoire Jacques-Louis Lions 2 Università degli Studi di Roma -La Sapienza- Rome

Abstract : We introduce a new class of -filtered- schemes for some first order non-linear Hamilton-Jacobi-Bellman equations. The work follows recent ideas of Froese and Oberman SIAM J. Numer. Anal., Vol 51, pp.423-444, 2013. The proposed schemes are not monotone but still satisfy some -monotone property. Convergence results and precise error estimates are given, of the order of √ ∆x where ∆x is the mesh size. The framework allows to construct finite difference discretizations that are easy to implement, high–order in the domains where the solution is smooth, and provably convergent, together with error estimates. Numerical tests on several examples are given to validate the approach, also showing how the filtered technique can be applied to stabilize an otherwise unstable high–order scheme.

Keywords : error estimates viscosity solutions high-order schemes monotone scheme Hamilton-Jacobi equation





Author: Olivier Bokanowski - Maurizio Falcone - Smita Sahu -

Source: https://hal.archives-ouvertes.fr/



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