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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2012
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| Acceso en línea: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00361429_v50_n5_p2497_DelPezzo http://hdl.handle.net/20.500.12110/paper_00361429_v50_n5_p2497_DelPezzo |
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paper:paper_00361429_v50_n5_p2497_DelPezzo2023-06-08T15:02:00Z Interior penalty discontinuous Galerkin FEM for the p(x)-Laplacian Del Pezzo, Leandro M. Lombardi, Ariel L. Martínez, Sandra Rita 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. 2012 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00361429_v50_n5_p2497_DelPezzo 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, Leandro M. Lombardi, Ariel L. Martínez, Sandra Rita 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. |
| author |
Del Pezzo, Leandro M. Lombardi, Ariel L. Martínez, Sandra Rita |
| author_facet |
Del Pezzo, Leandro M. Lombardi, Ariel L. Martínez, Sandra Rita |
| author_sort |
Del Pezzo, Leandro 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 |
| publishDate |
2012 |
| url |
https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00361429_v50_n5_p2497_DelPezzo http://hdl.handle.net/20.500.12110/paper_00361429_v50_n5_p2497_DelPezzo |
| work_keys_str_mv |
AT delpezzoleandrom interiorpenaltydiscontinuousgalerkinfemforthepxlaplacian AT lombardiariell interiorpenaltydiscontinuousgalerkinfemforthepxlaplacian AT martinezsandrarita interiorpenaltydiscontinuousgalerkinfemforthepxlaplacian |
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1768544123672854528 |