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Article

Vejchodský, Tomáš
On the quality of local flux reconstructions for guaranteed error bounds. (English). In: Brandts, J., Korotov, S., Křížek, M., Segeth, K., Šístek, J. and Vejchodský, T. (eds.): Application of Mathematics 2015, In honor of the birthday anniversaries of Ivo Babuška (90), Milan Práger (85), and Emil Vitásek (85). Proceedings. Prague, November 18-21, 2015. Institute of Mathematics CAS, Prague, 2015. pp. 242-255
MSC: 65N15, 65N30 | Zbl 06669935
Keywords:
a posteriori error estimates; complementarity; index of effectivity; elliptic problem; reaction-diffusion; singular perturbation
Summary:
In this contribution we consider elliptic problems of a reaction-diffusion type discretized by the finite element method and study the quality of guaranteed upper bounds of the error. In particular, we concentrate on complementary error bounds whose values are determined by suitable flux reconstructions. We present numerical experiments comparing the performance of the local flux reconstruction of Ainsworth and Vejchodsky [2] and the reconstruction of Braess and Schöberl [5]. We evaluate the efficiency of these flux reconstructions by their comparison with the optimal flux reconstruction computed as a global minimization problem.
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