Abstract:
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.
Registro:
Documento: |
Artículo
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Título: | Interior penalty discontinuous Galerkin FEM for the p(x)-Laplacian |
Autor: | Del Pezzo, L.M.; Lombardi, A.L.; Martínez, S. |
Filiación: | Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, 1428 Buenos Aires, Argentina Instituto de Ciencias, Universidad Nacional de General Sarmiento, J.M. Gutierrez 1150, B1613GSX Los Polvorines, Provincia de Buenos Aires, Argentina
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Palabras clave: | 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 |
Año: | 2012
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Volumen: | 50
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Número: | 5
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Página de inicio: | 2497
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Página de fin: | 2521
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DOI: |
http://dx.doi.org/10.1137/110820324 |
Título revista: | SIAM Journal on Numerical Analysis
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Título revista abreviado: | SIAM J Numer Anal
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ISSN: | 00361429
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CODEN: | SJNAA
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Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00361429_v50_n5_p2497_DelPezzo |
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Citas:
---------- APA ----------
Del Pezzo, L.M., Lombardi, A.L. & Martínez, S.
(2012)
. Interior penalty discontinuous Galerkin FEM for the p(x)-Laplacian. SIAM Journal on Numerical Analysis, 50(5), 2497-2521.
http://dx.doi.org/10.1137/110820324---------- CHICAGO ----------
Del Pezzo, L.M., Lombardi, A.L., Martínez, S.
"Interior penalty discontinuous Galerkin FEM for the p(x)-Laplacian"
. SIAM Journal on Numerical Analysis 50, no. 5
(2012) : 2497-2521.
http://dx.doi.org/10.1137/110820324---------- MLA ----------
Del Pezzo, L.M., Lombardi, A.L., Martínez, S.
"Interior penalty discontinuous Galerkin FEM for the p(x)-Laplacian"
. SIAM Journal on Numerical Analysis, vol. 50, no. 5, 2012, pp. 2497-2521.
http://dx.doi.org/10.1137/110820324---------- VANCOUVER ----------
Del Pezzo, L.M., Lombardi, A.L., Martínez, S. Interior penalty discontinuous Galerkin FEM for the p(x)-Laplacian. SIAM J Numer Anal. 2012;50(5):2497-2521.
http://dx.doi.org/10.1137/110820324