Fully computable robust a posteriori error bounds for singularly perturbed reaction-diffusion problems

0367487 - MÚ 2012 RIV DE eng J - Journal Article
Ainsworth, M. - Vejchodský, Tomáš
Fully computable robust a posteriori error bounds for singularly perturbed reaction-diffusion problems.
Numerische Mathematik. Roč. 119, č. 2 (2011), s. 219-243. ISSN 0029-599X. E-ISSN 0945-3245
R&D Projects: GA AV ČR IAA100760702; GA ČR(CZ) GA102/07/0496
Institutional research plan: CEZ:AV0Z10190503
Keywords : a posteriori error estimates * singularly perturbed problems * reaction-diffusion
Subject RIV: BA - General Mathematics
Impact factor: 1.321, year: 2011
http://www.springerlink.com/content/d384608709584278/

A procedure for the construction of robust, upper bounds for the error in the finite element approximation of singularly perturbed reaction–diffusion problems was presented in Ainsworth and Babuška (SIAM J Numer Anal 36(2):331–353, 1999) which entailed the solution of an infinite dimensional local boundary value problem. It is not possible to solve this problem exactly and this fact was recognised in the above work where it was indicated that the limitation would be addressed in a subsequent article. We view the present work as fulfilling that promise and as completing the investigation begun in Ainsworth and Babuška (SIAM J Numer Anal 36(2):331–353, 1999) by removing the obligation to solve a local problem exactly. The resulting new estimator is indeed fully computable and the first to provide fully computable, robust upper bounds in the setting of singularly perturbed problems discretised by the finite element method.
Permanent Link: http://hdl.handle.net/11104/0202150