INTERIOR PENALTY DISCONTINUOUS GALERKIN FEM FOR THE p(x)-LAPLACIAN

被引：12
|
作者：
Del Pezzo, Leandro M. [1 ]
Lombardi, Ariel L. [1 ,2 ]
Martinez, Sandra [1 ]
机构：
[1] Univ Buenos Aires, Fac Ciencias Exactas & Nat, Dept Matemat, RA-1428 Buenos Aires, DF, Argentina
[2] Univ Nacl Gen Sarmiento, Inst Ciencias, Los Polvorines, Buenos Aires, Argentina
来源：
SIAM JOURNAL ON NUMERICAL ANALYSIS | 2012年 / 50卷 / 05期
关键词：
variable exponent spaces; minimization; discontinuous Galerkin; SOBOLEV SPACES; GENERALIZED LEBESGUE; VARIABLE EXPONENT; EMBEDDINGS;
D O I：
10.1137/110820324
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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 : Omega -> [p1, p2] is log-Holder continuous and 1 < p(1) <= p(2) < infinity. 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 p(1) is close to one. This example is motivated by its applications to image processing.
引用
收藏
页码：2497 / 2521
页数：25
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