Finite difference schemes for the parabolic p-Laplace equation

• Félix del Teso ^[1] ; Erik Lindgren ^[2]
  1. [1] Universidad Autónoma de Madrid

     Universidad Autónoma de Madrid

     Madrid, España

     
  2. [2] Department of Mathematics, KTH-Royal Institute of Technology, Stockholm
• Localización: SeMA Journal: Boletín de la Sociedad Española de Matemática Aplicada, ISSN-e 2254-3902, ISSN 2254-3902, Vol. 80, Nº. 4, 2023, págs. 527-547
• Idioma: inglés
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• Resumen

  • 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.