Finite difference schemes for the parabolic p-Laplace equation
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We propose a new finite difference scheme for the degenerate parabolic equation ∂_t u - (|∇ 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 CFL-condition. 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.
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