Finite difference schemes for the parabolic p-Laplace equation

Abstract We propose a new finite difference scheme for the degenerate parabolic equation $$\begin{aligned} \partial _t u - \text{ div }(|\nabla u|^{p-2}\nabla u) =f, \quad p\ge 2. \end{aligned}$$ ? t u - div ( | ? p 2 ) = f , ? . Under assumption that data is Hölder continuous, we establish convergence of explicit-in-time Cauchy problem provided suitable stability type CFL-condition. An important advantage our approach, CFL-condition makes use regularity by to reduce computational cost. In particular, Lipschitz data, same order as heat and independent p .