Complementary error bounds for elliptic systems and applications

0391349 - MÚ 2014 RIV US eng J - Journal Article
Vejchodský, Tomáš
Complementary error bounds for elliptic systems and applications.
Applied Mathematics and Computation. Roč. 219, č. 3 (2013), s. 7194-7205. ISSN 0096-3003. E-ISSN 1873-5649
R&D Projects: GA AV ČR IAA100760702
Institutional support: RVO:67985840
Keywords : a posteriori error estimates * guaranteed * dual finite element methods
Subject RIV: BA - General Mathematics
Impact factor: 1.600, year: 2013
http://www.sciencedirect.com/science/article/pii/S0096300311007910

This contribution derives guaranteed upper bounds of the energy norm of the approximation error for linear elliptic partial differential systems. We generalize the complementarity error estimates known for scalar elliptic problems to general diffusion–convection–reaction linear elliptic systems. For systems we prove analogous properties of these error bounds as for the scalar case. A brief description how the presented general theory applies to linear elasticity is included as well as an application to chemical systems with reactions of at most first order. Numerical experiments showing the sharpness of the obtained upper bounds and their behavior in the adaptive procedure are presented, too.
Permanent Link: http://hdl.handle.net/11104/0220437