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

Authors:
M. Falcone;S. Finzi Vita;T. Giorgi;R. G. Smits
Affiliations:
Dipartimento di Matematica, Sapienza Universití di Roma, P.le Aldo Moro 2, 00185 Roma, Italy;Dipartimento di Matematica, Sapienza Universití di Roma, P.le Aldo Moro 2, 00185 Roma, Italy;Department of Mathematical Sciences, New Mexico State University, Las Cruces, NM 88003-8001, USA;Department of Mathematical Sciences, New Mexico State University, Las Cruces, NM 88003-8001, USA
Venue:
Applied Numerical Mathematics
Year:
2013

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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 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.