Maximum-norm a posteriori error estimates for singularly perturbed elliptic reaction-diffusion problems

被引：28
|
作者：
Demlow, Alan [1 ]
Kopteva, Natalia [2 ]
机构：
[1] Texas A&M Univ, Dept Math, Mail Stop 3368, College Stn, TX 77843 USA
[2] Univ Limerick, Dept Math & Stat, Limerick, Ireland
来源：
NUMERISCHE MATHEMATIK | 2016年 / 133卷 / 04期
基金：
美国国家科学基金会; 爱尔兰科学基金会;
关键词：
FINITE-ELEMENT-METHOD; INHOMOGENEOUS DIRICHLET; GRADED MESHES; EQUATION; APPROXIMATION; CONVERGENCE; PROPERTY; DOMAINS;
D O I：
10.1007/s00211-015-0763-0
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Residual-type a posteriori error estimates in the maximum norm are given for singularly perturbed semilinear reaction-diffusion equations posed in polyhedral domains. Standard finite element approximations are considered. The error constants are independent of the diameters of mesh elements and the small perturbation parameter. In our analysis, we employ sharp bounds on the Green's function of the linearized differential operator. Numerical results are presented that support our theoretical findings.
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页码：707 / 742
页数：36
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