Finite difference schemes for the parabolic p-Laplace equation

2022/05/26 by Félix del Teso, Erik Lindgren, del Teso, Félix +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Equations and Numerical Methods #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.2205.13656

openalex publication_date 2022/05/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We propose a new finite difference scheme for the degenerate parabolic equation ∂_t u - 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 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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