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Numerische Mathematik

, Volume 137, Issue 3, pp 607–642 | Cite as

Energy-norm a posteriori error estimates for singularly perturbed reaction-diffusion problems on anisotropic meshes

  • Natalia KoptevaEmail author
Article

Abstract

Residual-type a posteriori error estimates in the energy norm are given for singularly perturbed semilinear reaction-diffusion equations posed in polygonal domains. Linear finite elements are considered on anisotropic triangulations. The error constants are independent of the diameters and the aspect ratios of mesh elements and of the small perturbation parameter. To deal with anisotropic triangulations, a special quasi-interpolation operator is employed that may be of independent interest.

Mathematics Subject Classification

65N15 65N30 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsUniversity of LimerickLimerickIreland

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