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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| 008 | 190411s2012 xx ||||fo|||| 00| 0 eng|d | ||
| 024 | 7 | |2 scopus |a 2-s2.0-84868355657 | |
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| 030 | |a SJNAA | ||
| 100 | 1 | |a Del Pezzo, L.M. | |
| 245 | 1 | 0 | |a Interior penalty discontinuous Galerkin FEM for the p(x)-Laplacian |
| 260 | |c 2012 | ||
| 270 | 1 | 0 | |m Del Pezzo, L.M.; Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, 1428 Buenos Aires, Argentina; email: ldpezzo@dm.uba.ar |
| 506 | |2 openaire |e Política editorial | ||
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| 520 | 3 | |a 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. |l eng | |
| 593 | |a Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, 1428 Buenos Aires, Argentina | ||
| 593 | |a Instituto de Ciencias, Universidad Nacional de General Sarmiento, J.M. Gutierrez 1150, B1613GSX Los Polvorines, Provincia de Buenos Aires, Argentina | ||
| 690 | 1 | 0 | |a DISCONTINUOUS GALERKIN |
| 690 | 1 | 0 | |a MINIMIZATION |
| 690 | 1 | 0 | |a VARIABLE EXPONENT SPACES |
| 690 | 1 | 0 | |a DISCONTINUOUS GALERKIN |
| 690 | 1 | 0 | |a DISCONTINUOUS GALERKIN FEM |
| 690 | 1 | 0 | |a DISCONTINUOUS GALERKIN METHODS |
| 690 | 1 | 0 | |a NUMERICAL EXPERIMENTS |
| 690 | 1 | 0 | |a P (X)-LAPLACIAN |
| 690 | 1 | 0 | |a VARIABLE EXPONENTS |
| 690 | 1 | 0 | |a VARIATIONAL PROBLEMS |
| 690 | 1 | 0 | |a IMAGE PROCESSING |
| 690 | 1 | 0 | |a LAPLACE TRANSFORMS |
| 690 | 1 | 0 | |a NUMERICAL METHODS |
| 690 | 1 | 0 | |a OPTIMIZATION |
| 690 | 1 | 0 | |a GALERKIN METHODS |
| 700 | 1 | |a Lombardi, A.L. | |
| 700 | 1 | |a Martínez, S. | |
| 773 | 0 | |d 2012 |g v. 50 |h pp. 2497-2521 |k n. 5 |p SIAM J Numer Anal |x 00361429 |w (AR-BaUEN)CENRE-263 |t SIAM Journal on Numerical Analysis | |
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| 856 | 4 | 0 | |u https://doi.org/10.1137/110820324 |y DOI |
| 856 | 4 | 0 | |u https://hdl.handle.net/20.500.12110/paper_00361429_v50_n5_p2497_DelPezzo |y Handle |
| 856 | 4 | 0 | |u https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00361429_v50_n5_p2497_DelPezzo |y Registro en la Biblioteca Digital |
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