A Finite Difference Method for the Variational p-Laplacian
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...
| Autores: | , |
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| Formato: | artículo |
| Fecha de publicación: | 2022 |
| País: | España |
| Recursos: | Universidad Complutense de Madrid (UCM) |
| Repositorio: | Docta Complutense |
| Idioma: | inglés |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/71302 |
| Acesso em linha: | https://hdl.handle.net/20.500.14352/71302 |
| Access Level: | acceso abierto |
| Palavra-chave: | p-Laplacian Finite difference Mean value property Nonhomogeneous Dirichlet problem Viscosity solutions Dynamic programming principle Análisis matemático 1202 Análisis y Análisis Funcional |
| Resumo: | 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. |
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