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This article is cited in 3 scientific papers (total in 3 papers)
General numerical methods
A note on a posteriori error bounds for numerical solutions of elliptic equations with a piecewise constant reaction coefficient having large jumps
V. G. Korneev St. Petersburg State University, St. Petersburg, 199034 Russia
Abstract:
We have derived guaranteed, robust, and fully computable a posteriori error bounds for approximate solutions of the equation $\Delta \Delta u + {{\Bbbk }^{2}}u = f$, where the coefficient $\Bbbk \geqslant 0$ is a constant in each subdomain (finite element) and chaotically varies between subdomains in a sufficiently wide range. For finite element solutions, these bounds are robust with respect to $\Bbbk \in [0,{\text{c}}{{{\text{h}}}^{{ - 2}}}]$, $c={\text{const}}$ , and possess some other good features. The coefficients in front of two typical norms on their right-hand sides are only insignificantly worse than those obtained earlier for $\Bbbk \equiv {\text{const}}{\text{.}}$ The bounds can be calculated without resorting to the equilibration procedures, and they are sharp for at least low-order methods. The derivation technique used in this paper is similar to the one used in our preceding papers (2017–2019) for obtaining a posteriori error bounds that are not improvable in the order of accuracy.
Key words:
a posteriori error bounds, singularly perturbed fourth-order elliptic equations, piecewise constant reaction coefficient, finite element method, sharp bounds.
Received: 23.10.2019 Revised: 28.05.2020 Accepted: 07.07.2020
Citation:
V. G. Korneev, “A note on a posteriori error bounds for numerical solutions of elliptic equations with a piecewise constant reaction coefficient having large jumps”, Zh. Vychisl. Mat. Mat. Fiz., 60:11 (2020), 1815–1822; Comput. Math. Math. Phys., 60:11 (2020), 1754–1760
Linking options:
https://www.mathnet.ru/eng/zvmmf11154 https://www.mathnet.ru/eng/zvmmf/v60/i11/p1815
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Abstract page: | 69 | References: | 12 |
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