On the accuracy of a posteriori functional error majorants for approximate solutions of elliptic equations
- Authors: Korneev V.G.1
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Affiliations:
- St. Petersburg State University
- Issue: Vol 96, No 1 (2017)
- Pages: 380-383
- Section: Mathematics
- URL: https://journals.rcsi.science/1064-5624/article/view/225296
- DOI: https://doi.org/10.1134/S1064562417040287
- ID: 225296
Cite item
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.
About the authors
V. G. Korneev
St. Petersburg State University
Author for correspondence.
Email: vad.korneev2011@yandex.ru
Russian Federation, St. Petersburg