We present and analyze an approximation scheme for the two-dimensional game p-Laplacian in the framework of viscosity solutions. The approximation is based on a semiLagrangian scheme which exploits the idea of p-averages. We study the properties of the scheme and prove that it converges, in particular cases, to the viscosity solution of the game p-Laplacian. We also present a numerical implementation of the scheme for different values of p; the numerical tests show that the scheme is accurate. (C) 2012 IMACS. Published by Elsevier B.V. All rights reserved.

A semi-Lagrangian scheme for the game p-Laplacian via p-averaging / Falcone, Maurizio; FINZI VITA, Stefano; T., Giorgi; R. G., Smits. - In: APPLIED NUMERICAL MATHEMATICS. - ISSN 0168-9274. - STAMPA. - 73:(2013), pp. 63-80. [10.1016/j.apnum.2012.11.006]

A semi-Lagrangian scheme for the game p-Laplacian via p-averaging

FALCONE, Maurizio;FINZI VITA, Stefano;
2013

Abstract

We present and analyze an approximation scheme for the two-dimensional game p-Laplacian in the framework of viscosity solutions. The approximation is based on a semiLagrangian scheme which exploits the idea of p-averages. We study the properties of the scheme and prove that it converges, in particular cases, to the viscosity solution of the game p-Laplacian. We also present a numerical implementation of the scheme for different values of p; the numerical tests show that the scheme is accurate. (C) 2012 IMACS. Published by Elsevier B.V. All rights reserved.
2013
convergence; hamilton-jacobi equations; p-laplacian; semi-lagrangian schemes; tug of war game; viscosity solutions
01 Pubblicazione su rivista::01a Articolo in rivista
A semi-Lagrangian scheme for the game p-Laplacian via p-averaging / Falcone, Maurizio; FINZI VITA, Stefano; T., Giorgi; R. G., Smits. - In: APPLIED NUMERICAL MATHEMATICS. - ISSN 0168-9274. - STAMPA. - 73:(2013), pp. 63-80. [10.1016/j.apnum.2012.11.006]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/506949
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