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MSC: 65N15, 65N30
complementarity; guaranteed upper error bounds; method of hypercircle; a posteriori error estimates; error majorants
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.
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