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

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    0505170 - MÚ 2020 RIV CH eng J - Článek v odborném periodiku
    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
    Grant CEP: GA ČR(CZ) GA18-09628S
    Institucionální podpora: RVO:67985840
    Klíčová slova: finite element analysis * singularly perturbed problems * flux reconstruction
    Kód oboru RIV: BA - Obecná matematika
    Obor OECD: Pure mathematics
    Impakt faktor: 5.763, rok: 2019
    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.
    Trvalý link: http://hdl.handle.net/11104/0296668
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