This paper presents a review of the complementary technique with the emphasis on computable and guaranteed upper bounds of the approximation error. For simplicity, the approach is described on a numerical solution of the Poisson problem. We derive the complementary error bounds, prove their fundamental properties, present the method of hypercircle, mention possible generalizations and show a couple of numerical examples.
@article{702760,
title = {Complementarity - the way towards guaranteed error estimates},
booktitle = {Programs and Algorithms of Numerical Mathematics},
series = {GDML\_Books},
publisher = {Institute of Mathematics AS CR},
address = {Prague},
year = {2010},
pages = {205-220},
url = {http://dml.mathdoc.fr/item/702760}
}
Vejchodský, Tomáš. Complementarity - the way towards guaranteed error estimates, dans Programs and Algorithms of Numerical Mathematics, GDML_Books, (2010), pp. 205-220. http://gdmltest.u-ga.fr/item/702760/