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Numerische Mathematik

, Volume 133, Issue 4, pp 707–742 | Cite as

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

  • Alan Demlow
  • Natalia KoptevaEmail author
Article

Abstract

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.

Mathematics Subject Classification

65N15 65N30 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Department of MathematicsTexas A&M UniversityCollege StationUSA
  2. 2.Department of Mathematics and StatisticsUniversity of LimerickLimerickIreland

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