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.

EUDML-ID : urn:eudml:doc:271283
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Mots clés:

@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/