A simple approach to reliable and robust a posteriori error estimation for singularly perturbed problems

0505170 - MÚ 2020 RIV CH eng J - Journal Article
Ainsworth, M. - Vejchodský, Tomáš
A simple approach to reliable and robust a posteriori error estimation for singularly perturbed problems.
Computer Methods in Applied Mechanics and Engineering. Roč. 353, 15 August (2019), s. 373-390. ISSN 0045-7825. E-ISSN 1879-2138
R&D Projects: GA ČR(CZ) GA18-09628S
Institutional support: RVO:67985840
Keywords : finite element analysis * singularly perturbed problems * flux reconstruction
OECD category: Pure mathematics
Impact factor: 5.763, year: 2019
Method of publishing: Limited access
http://dx.doi.org/10.1016/j.cma.2019.05.014

A simple flux reconstruction for finite element solutions of reaction-diffusion problems is shown to yield fully computable upper bounds on the energy norm of error in an approximation of singularly perturbed reaction-diffusion problem. The flux reconstruction is based on simple, independent post-processing operations over patches of elements in conjunction with standard Raviart-Thomas vector fields. We prove that the corresponding local error indicators are locally efficient and robust (up to a nonstandard oscillation term) with respect to any mesh size and any size of the reaction coefficient, including the singularly perturbed limit.
Permanent Link: http://hdl.handle.net/11104/0296668