Improved energy-norm a posteriori error estimates for singularly perturbed reaction-diffusion problems on anisotropic meshes
Numerical Analysis
2020-04-07 v5 Numerical Analysis
Abstract
In the recent article [Kopteva, N., 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 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.
Keywords
Cite
@article{arxiv.1810.09211,
title = {Improved energy-norm a posteriori error estimates for singularly perturbed reaction-diffusion problems on anisotropic meshes},
author = {Natalia Kopteva},
journal= {arXiv preprint arXiv:1810.09211},
year = {2020}
}