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An approximation scheme for an Eikonal Equation with discontinuous coefficient

Abstract : We consider the stationary Hamilton-Jacobi equation where the dynamics can vanish at some points, the cost function is strictly positive and is allowed to be discontinuous. More precisely, we consider special class of discontinuities for which the notion of viscosity solution is well-suited. We propose a semi-Lagrangian scheme for the numerical approximation of the viscosity solution in the sense of Ishii and we study its properties. We also prove an a-priori error estimate for the scheme in an integral norm. The last section contains some applications to control and image processing problems.
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https://hal.inria.fr/hal-01067426
Contributor : Estelle Bouzat <>
Submitted on : Tuesday, September 23, 2014 - 2:08:04 PM
Last modification on : Wednesday, July 3, 2019 - 10:48:04 AM

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Adriano Festa, Maurizio Falcone. An approximation scheme for an Eikonal Equation with discontinuous coefficient. SIAM Journal on Numerical Analysis, Society for Industrial and Applied Mathematics, 2014, 52 (1), pp.236-257. ⟨10.1137/120901829⟩. ⟨hal-01067426⟩

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