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

Autor:	Falcone, M., Vita, S. Finzi, Giorgi, T., Smits, R. G.
Rok vydání:	2013
Předmět:	Mathematics - Numerical Analysis
Druh dokumentu:	Working Paper
DOI:	10.1016/j.apnum.2012.11.006
Popis:	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 semi-Lagrangian 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. Comment: 34 pages, 3 figures. To appear on Applied Numerical Mathematics
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1301.7570 Zobrazit plný text záznamu View this record from Arxiv