Del Teso Méndez, Félix

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Del Teso Méndez
Universidad Complutense de Madrid
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Ciencias Químicas
Análisis Matemático Matemática Aplicada
Matemática Aplicada
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  • Publication
    A Finite Difference Method for the Variational p-Laplacian
    (Springer, 2022) Del Teso Méndez, Félix; Lindgren, Erik
    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.