Resumen de Finite difference schemes for the parabolic p-Laplace equation

Félix del Teso Méndez, Erik Lindgren

• We propose a new finite difference scheme for the degenerate parabolic equation ∂tu − div(|∇u|p−2∇u) = f , p ≥ 2.

  Under the assumption that the data is Hölder continuous, we establish the convergence of the explicit-in-time scheme for the Cauchy problem provided a suitable stability type CFLcondition. An important advantage of our approach, is that the CFL-condition makes use of the regularity provided by the scheme to reduce the computational cost. In particular, for Lipschitz data, the CFL-condition is of the same order as for the heat equation and independent of p.