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IMA Journal of Numerical Analysis Advance Access originally published online on November 18, 2005
IMA Journal of Numerical Analysis 2006 26(3):525-540; doi:10.1093/imanum/dri043
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© The author 2005. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Guaranteed and locally computable a posteriori error estimate

Tomás Vejchodsky**

Mathematical Institute, Academy of Sciences, Zitná 25, CZ–115 67 Prague 1, Czech Republic

** Email: vejchod{at}math.cas.cz

A new approach, based on the combination of the equilibrated residual method and the method of hypercircle, is proposed for a posteriori error estimation. Computer implementation of the equilibrated residual method is fast, but it does not produce guaranteed estimates. On the other hand, the method of hypercircle delivers guaranteed estimates, but it is not fast because it involves solving a global linear algebraic system. The combination of these two methods leads to guaranteed and locally computable a posteriori error estimator. This combined method is applied to linear elliptic problem in two dimensions with mixed boundary conditions and non-negative absolute terms.

Key Words: a posteriori error estimates; linear elliptic problem; finite-element method; equilibrated residual method; method of hypercircle

Received on 14 July 2004. Revised on 9 April 2005.


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