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...

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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
id todo:paper_00361429_v50_n5_p2497_DelPezzo
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spelling todo:paper_00361429_v50_n5_p2497_DelPezzo2023-10-03T14:47:45Z Interior penalty discontinuous Galerkin FEM for the p(x)-Laplacian Del Pezzo, L.M. Lombardi, A.L. Martínez, S. 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 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. Fil:Del Pezzo, L.M. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Lombardi, A.L. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Martínez, S. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_00361429_v50_n5_p2497_DelPezzo
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic 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
spellingShingle 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
Del Pezzo, L.M.
Lombardi, A.L.
Martínez, S.
Interior penalty discontinuous Galerkin FEM for the p(x)-Laplacian
topic_facet 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
description 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.
format JOUR
author Del Pezzo, L.M.
Lombardi, A.L.
Martínez, S.
author_facet Del Pezzo, L.M.
Lombardi, A.L.
Martínez, S.
author_sort Del Pezzo, L.M.
title Interior penalty discontinuous Galerkin FEM for the p(x)-Laplacian
title_short Interior penalty discontinuous Galerkin FEM for the p(x)-Laplacian
title_full Interior penalty discontinuous Galerkin FEM for the p(x)-Laplacian
title_fullStr Interior penalty discontinuous Galerkin FEM for the p(x)-Laplacian
title_full_unstemmed Interior penalty discontinuous Galerkin FEM for the p(x)-Laplacian
title_sort interior penalty discontinuous galerkin fem for the p(x)-laplacian
url http://hdl.handle.net/20.500.12110/paper_00361429_v50_n5_p2497_DelPezzo
work_keys_str_mv AT delpezzolm interiorpenaltydiscontinuousgalerkinfemforthepxlaplacian
AT lombardial interiorpenaltydiscontinuousgalerkinfemforthepxlaplacian
AT martinezs interiorpenaltydiscontinuousgalerkinfemforthepxlaplacian
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