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

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conference contribution
posted on 2020-10-15, 13:19 authored by Natalia KoptevaNatalia Kopteva
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.

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Publication

Boundary and Interior Layers, Computational and Asymptotic Methods,Barrenechea G., Mackenzie J. (eds) Lecture Notes in Computational Science and Engineering;135

Publisher

Springer

Note

peer-reviewed

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The original publication is available at www.springerlink.com

Language

English

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