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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
