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

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Abstract

In the recent article (Kopteva, Numer Math 137:607–642, 2017) the author obtained residual-type a posteriori error estimates in the energy norm for singularly perturbed semilinear reaction-diffusion equations on unstructured anisotropic triangulations. The error constants in these estimates are independent of the diameters and the aspect ratios of mesh elements and of the small perturbation parameter. The purpose of this note is to improve the weights in the jump residual part of the estimator. This is attained by using a novel sharper version of the scaled trace theorem for anisotropic elements, in which the hat basis functions are involved as weights.

Original languageEnglish
Title of host publicationBoundary and Interior Layers, Computational and Asymptotic Methods, BAIL 2018
EditorsGabriel R. Barrenechea, John Mackenzie
PublisherSpringer
Pages143-156
Number of pages14
ISBN (Print)9783030417994
DOIs
Publication statusPublished - 2020
EventInternational Conference on Boundary and Interior Layers, BAIL 2018 - Glasgow, United Kingdom
Duration: 18 Jun 201822 Jun 2018

Publication series

NameLecture Notes in Computational Science and Engineering
Volume135
ISSN (Print)1439-7358
ISSN (Electronic)2197-7100

Conference

ConferenceInternational Conference on Boundary and Interior Layers, BAIL 2018
Country/TerritoryUnited Kingdom
CityGlasgow
Period18/06/1822/06/18

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