Interior penalty discontinuous Galerkin FEM for the p(x)-Laplacian

In this paper we construct an "interior penalty" discontinuous Galerkin method to approximate the minimizer of a variational problem related to the p(x)-Laplacian. The function p: Ω → [p1,p2] is log-Holder continuous and 1 < p1 ≤ p2 ≤ ∞. We prove that the minimizers of the discrete func...

Descripción completa

Guardado en:
Detalles Bibliográficos
Autores principales: Del Pezzo, L.M., Lombardi, A.L., Martínez, S.
Formato: JOUR
Materias:
Discontinuous Galerkin
Minimization
Variable exponent spaces
Discontinuous galerkin
Discontinuous Galerkin FEM
Discontinuous Galerkin methods
Numerical experiments
P (x)-Laplacian
Variable exponents
Variational problems
Image processing
Laplace transforms
Numerical methods
Optimization
Galerkin methods
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_00361429_v50_n5_p2497_DelPezzo
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
Descripción
Sumario:In this paper we construct an "interior penalty" discontinuous Galerkin method to approximate the minimizer of a variational problem related to the p(x)-Laplacian. The function p: Ω → [p1,p2] is log-Holder continuous and 1 < p1 ≤ p2 ≤ ∞. We prove that the minimizers of the discrete functional converge to the solution. We also make some numerical experiments in dimension one to compare this method with the conforming Galerkin method, in the case where p1 is close to one. This example is motivated by its applications to image processing. © 2012 Society for Industrial and Applied Mathematics.

Ejemplares similares