Standard

On a Renewed Approach to A Posteriori Error Bounds for Approximate Solutions of Reaction-Diffusion Equations. / Korneev, Vadim G.

Advanced Finite Element Methods with Applications - Selected Papers from the 30th Chemnitz Finite Element Symposium 2017. ред. / Thomas Apel; Ulrich Langer; Arnd Meyer; Olaf Steinbach. Springer Nature, 2019. стр. 221-245 (Lecture Notes in Computational Science and Engineering; Том 128).

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Harvard

Korneev, VG 2019, On a Renewed Approach to A Posteriori Error Bounds for Approximate Solutions of Reaction-Diffusion Equations. в T Apel, U Langer, A Meyer & O Steinbach (ред.), Advanced Finite Element Methods with Applications - Selected Papers from the 30th Chemnitz Finite Element Symposium 2017. Lecture Notes in Computational Science and Engineering, Том. 128, Springer Nature, стр. 221-245, 30th Chemnitz Finite Element Symposium, 2017, St. Wolfgang, Австрия, 25/09/17. https://doi.org/10.1007/978-3-030-14244-5_12

APA

Korneev, V. G. (2019). On a Renewed Approach to A Posteriori Error Bounds for Approximate Solutions of Reaction-Diffusion Equations. в T. Apel, U. Langer, A. Meyer, & O. Steinbach (Ред.), Advanced Finite Element Methods with Applications - Selected Papers from the 30th Chemnitz Finite Element Symposium 2017 (стр. 221-245). (Lecture Notes in Computational Science and Engineering; Том 128). Springer Nature. https://doi.org/10.1007/978-3-030-14244-5_12

Vancouver

Korneev VG. On a Renewed Approach to A Posteriori Error Bounds for Approximate Solutions of Reaction-Diffusion Equations. в Apel T, Langer U, Meyer A, Steinbach O, Редакторы, Advanced Finite Element Methods with Applications - Selected Papers from the 30th Chemnitz Finite Element Symposium 2017. Springer Nature. 2019. стр. 221-245. (Lecture Notes in Computational Science and Engineering). https://doi.org/10.1007/978-3-030-14244-5_12

Author

Korneev, Vadim G. / On a Renewed Approach to A Posteriori Error Bounds for Approximate Solutions of Reaction-Diffusion Equations. Advanced Finite Element Methods with Applications - Selected Papers from the 30th Chemnitz Finite Element Symposium 2017. Редактор / Thomas Apel ; Ulrich Langer ; Arnd Meyer ; Olaf Steinbach. Springer Nature, 2019. стр. 221-245 (Lecture Notes in Computational Science and Engineering).

BibTeX

@inproceedings{39ab78e7f5d04e98a9c120b97cdbf280,
title = "On a Renewed Approach to A Posteriori Error Bounds for Approximate Solutions of Reaction-Diffusion Equations",
abstract = "We discuss a new approach to obtaining the guaranteed, robust and consistent a posteriori error bounds for approximate solutions of the reaction-diffusion problems, modelled by the equation − Δu + σu = f in Ω, u|∂Ω = 0, with an arbitrary constant or piece wise constant σ ≥ 0. The consistency of a posteriori error bounds for solutions by the finite element methods assumes in this paper that their orders of accuracy in respect to the mesh size h coincide with those in the corresponding sharp a priori bounds. Additionally, it assumes that for such a coincidence it is sufficient that the testing fluxes possess only the standard approximation properties without resorting to the equilibration. Under mild assumptions, with the use of a new technique, it is proved that the coefficient before the L2-norm of the residual type term in the a posteriori error bound is O(h) uniformly for all testing fluxes from admissible set, which is the space H(Ω, div). As a consequence of these facts, there is a wide range of computationally cheap and efficient procedures for evaluating the test fluxes, making the obtained a posteriori error bounds sharp. The technique of obtaining the consistent a posteriori bounds was exposed in [arXiv:1711.02054v1 [math.NA] 6 Nov 2017] and very briefly in [Doklady Mathematics, 96 (1), 2017, 380–383].",
author = "Korneev, {Vadim G.}",
note = "Publisher Copyright: {\textcopyright} Springer Nature Switzerland AG 2019. Copyright: Copyright 2019 Elsevier B.V., All rights reserved.; 30th Chemnitz Finite Element Symposium, 2017 ; Conference date: 25-09-2017 Through 27-09-2017",
year = "2019",
doi = "10.1007/978-3-030-14244-5_12",
language = "English",
isbn = "9783030142438",
series = "Lecture Notes in Computational Science and Engineering",
publisher = "Springer Nature",
pages = "221--245",
editor = "Thomas Apel and Ulrich Langer and Arnd Meyer and Olaf Steinbach",
booktitle = "Advanced Finite Element Methods with Applications - Selected Papers from the 30th Chemnitz Finite Element Symposium 2017",
address = "Germany",

}

RIS

TY - GEN

T1 - On a Renewed Approach to A Posteriori Error Bounds for Approximate Solutions of Reaction-Diffusion Equations

AU - Korneev, Vadim G.

N1 - Publisher Copyright: © Springer Nature Switzerland AG 2019. Copyright: Copyright 2019 Elsevier B.V., All rights reserved.

PY - 2019

Y1 - 2019

N2 - We discuss a new approach to obtaining the guaranteed, robust and consistent a posteriori error bounds for approximate solutions of the reaction-diffusion problems, modelled by the equation − Δu + σu = f in Ω, u|∂Ω = 0, with an arbitrary constant or piece wise constant σ ≥ 0. The consistency of a posteriori error bounds for solutions by the finite element methods assumes in this paper that their orders of accuracy in respect to the mesh size h coincide with those in the corresponding sharp a priori bounds. Additionally, it assumes that for such a coincidence it is sufficient that the testing fluxes possess only the standard approximation properties without resorting to the equilibration. Under mild assumptions, with the use of a new technique, it is proved that the coefficient before the L2-norm of the residual type term in the a posteriori error bound is O(h) uniformly for all testing fluxes from admissible set, which is the space H(Ω, div). As a consequence of these facts, there is a wide range of computationally cheap and efficient procedures for evaluating the test fluxes, making the obtained a posteriori error bounds sharp. The technique of obtaining the consistent a posteriori bounds was exposed in [arXiv:1711.02054v1 [math.NA] 6 Nov 2017] and very briefly in [Doklady Mathematics, 96 (1), 2017, 380–383].

AB - We discuss a new approach to obtaining the guaranteed, robust and consistent a posteriori error bounds for approximate solutions of the reaction-diffusion problems, modelled by the equation − Δu + σu = f in Ω, u|∂Ω = 0, with an arbitrary constant or piece wise constant σ ≥ 0. The consistency of a posteriori error bounds for solutions by the finite element methods assumes in this paper that their orders of accuracy in respect to the mesh size h coincide with those in the corresponding sharp a priori bounds. Additionally, it assumes that for such a coincidence it is sufficient that the testing fluxes possess only the standard approximation properties without resorting to the equilibration. Under mild assumptions, with the use of a new technique, it is proved that the coefficient before the L2-norm of the residual type term in the a posteriori error bound is O(h) uniformly for all testing fluxes from admissible set, which is the space H(Ω, div). As a consequence of these facts, there is a wide range of computationally cheap and efficient procedures for evaluating the test fluxes, making the obtained a posteriori error bounds sharp. The technique of obtaining the consistent a posteriori bounds was exposed in [arXiv:1711.02054v1 [math.NA] 6 Nov 2017] and very briefly in [Doklady Mathematics, 96 (1), 2017, 380–383].

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U2 - 10.1007/978-3-030-14244-5_12

DO - 10.1007/978-3-030-14244-5_12

M3 - Conference contribution

AN - SCOPUS:85069163824

SN - 9783030142438

T3 - Lecture Notes in Computational Science and Engineering

SP - 221

EP - 245

BT - Advanced Finite Element Methods with Applications - Selected Papers from the 30th Chemnitz Finite Element Symposium 2017

A2 - Apel, Thomas

A2 - Langer, Ulrich

A2 - Meyer, Arnd

A2 - Steinbach, Olaf

PB - Springer Nature

T2 - 30th Chemnitz Finite Element Symposium, 2017

Y2 - 25 September 2017 through 27 September 2017

ER -

ID: 71957691