A Finite Difference Method for the Variational p-Laplacian

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Del Teso Méndez, Félix and Lindgren, Erik (2022) A Finite Difference Method for the Variational p-Laplacian. Journal of Scientific Computing, 90 (1). ISSN 0885-7474

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Official URL: https://doi.org/10.1007/s10915-021-01745-z



Abstract

We propose a new monotone finite difference discretization for the variational p-Laplace operator, pu = div(|∇u|p−2∇u), and present a convergent numerical scheme for related Dirichlet problems. The resulting nonlinear system is solved using two different methods: one based on Newton-Raphson and one explicit method. Finally, we exhibit some numerical simulations supporting our theoretical results. To the best of our knowledge, this is the first monotone finite difference discretization of the variational p-Laplacian and also the first time that nonhomogeneous problems for this operator can be treated numerically with a finite difference scheme.


Item Type:Article
Additional Information:

CRUE-CSIC (Acuerdos Transformativos 2021)

Uncontrolled Keywords:p-Laplacian, Finite difference, Mean value property, Nonhomogeneous Dirichlet problem, Viscosity solutions, Dynamic programming principle
Subjects:Sciences > Mathematics > Mathematical analysis
ID Code:70323
Deposited On:24 Feb 2022 09:04
Last Modified:24 Feb 2022 09:05

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