A semi-Lagrangian scheme for the game $p$-Laplacian via $p$-averaging
Numerical Analysis
2013-02-01 v1
Abstract
We present and analyze an approximation scheme for the two-dimensional game -Laplacian in the framework of viscosity solutions. The approximation is based on a semi-Lagrangian scheme which exploits the idea of -averages. We study the properties of the scheme and prove that it converges, in particular cases, to the viscosity solution of the game -Laplacian. We also present a numerical implementation of the scheme for different values of ; the numerical tests show that the scheme is accurate.
Keywords
Cite
@article{arxiv.1301.7570,
title = {A semi-Lagrangian scheme for the game $p$-Laplacian via $p$-averaging},
author = {M. Falcone and S. Finzi Vita and T. Giorgi and R. G. Smits},
journal= {arXiv preprint arXiv:1301.7570},
year = {2013}
}
Comments
34 pages, 3 figures. To appear on Applied Numerical Mathematics