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On the accuracy of a posteriori functional error majorants for approximate solutions of elliptic equations

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Abstract

A new a posteriori functional majorant is obtained for the error of approximate solutions to an elliptic equation of order 2n, n ≥ 1, with an arbitrary nonnegative constant coefficient σ ≥ 0 in the lowest order term σu, where u is the solution of the equation. The majorant is much more accurate than Aubin’s majorant, which makes no sense at σ ≡ 0 and coarsens the error estimate for σ from a significant neighborhood of zero. The new majorant also surpasses other majorants having been obtained for the case σ ≡ 0 over recent decades. For solutions produced by the finite element method on quasi-uniform grids, it is shown that the new a posteriori majorant is sharp in order of accuracy, which coincides with that of sharp a priori error estimates.

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Authors and Affiliations

  1. St. Petersburg State University, St. Petersburg, Russia

    V. G. Korneev

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  1. V. G. Korneev
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Correspondence to V. G. Korneev.

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Original Russian Text © V.G. Korneev, 2017, published in Doklady Akademii Nauk, 2017, Vol. 475, No. 6, pp. 605–608.

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Korneev, V.G. On the accuracy of a posteriori functional error majorants for approximate solutions of elliptic equations. Dokl. Math. 96, 380–383 (2017). https://doi.org/10.1134/S1064562417040287

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