IP-DGFEM method for the $p(x)$-Laplacian

DEL PEZZO, LEANDRO; LOMBARDI, ARIEL; MARTÍNEZ, SANDRA RITA

SIAM JOURNAL ON NUMERICAL ANALYSIS

SIAM PUBLICATIONS

Lugar: Philadelphia-USA; Año: 2012

0036-1429

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 H¨lder 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.