A Note on a Posteriori Error Bounds for Numerical Solutions of Elliptic Equations with a Piecewise Constant Reaction Coefficient Having Large Jumps

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A Note on a Posteriori Error Bounds for Numerical Solutions of Elliptic Equations with a Piecewise Constant Reaction Coefficient Having Large Jumps. / Korneev, V. G.

в: Computational Mathematics and Mathematical Physics, Том 60, № 11, 01.11.2020, стр. 1754-1760.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

BibTeX

@article{b68bd5916ff64b1bbe77d1588bb90a3d,

title = "A Note on a Posteriori Error Bounds for Numerical Solutions of Elliptic Equations with a Piecewise Constant Reaction Coefficient Having Large Jumps",

abstract = "Abstract: We have derived guaranteed, robust, and fully computable a posteriori error bounds for approximate solutions of the equation ΔΔu + k2u = f, where the coefficient k ≥ 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 k ∈[0, ch−2] c = 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 k ≡ const. 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.",

keywords = "a posteriori error bounds, finite element method, piecewise constant reaction coefficient, sharp bounds, singularly perturbed fourth-order elliptic equations, FINITE-ELEMENT APPROXIMATION, GALERKIN APPROXIMATIONS, ESTIMATOR, PLATE",

author = "Korneev, {V. G.}",

year = "2020",

month = nov,

day = "1",

doi = "10.1134/S096554252011007X",

language = "English",

volume = "60",

pages = "1754--1760",

journal = "Computational Mathematics and Mathematical Physics",

issn = "0965-5425",

publisher = "МАИК {"}Наука/Интерпериодика{"}",

number = "11",

}

RIS

TY - JOUR

T1 - A Note on a Posteriori Error Bounds for Numerical Solutions of Elliptic Equations with a Piecewise Constant Reaction Coefficient Having Large Jumps

AU - Korneev, V. G.

PY - 2020/11/1

Y1 - 2020/11/1

N2 - Abstract: We have derived guaranteed, robust, and fully computable a posteriori error bounds for approximate solutions of the equation ΔΔu + k2u = f, where the coefficient k ≥ 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 k ∈[0, ch−2] c = 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 k ≡ const. 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.

AB - Abstract: We have derived guaranteed, robust, and fully computable a posteriori error bounds for approximate solutions of the equation ΔΔu + k2u = f, where the coefficient k ≥ 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 k ∈[0, ch−2] c = 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 k ≡ const. 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.

KW - a posteriori error bounds

KW - finite element method

KW - piecewise constant reaction coefficient

KW - sharp bounds

KW - singularly perturbed fourth-order elliptic equations

KW - FINITE-ELEMENT APPROXIMATION

KW - GALERKIN APPROXIMATIONS

KW - ESTIMATOR

KW - PLATE

UR - http://www.scopus.com/inward/record.url?scp=85097312368&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/e49aa33c-18e2-30c4-bff8-053cdf5dad8d/

U2 - 10.1134/S096554252011007X

DO - 10.1134/S096554252011007X

M3 - Article

AN - SCOPUS:85097312368

VL - 60

SP - 1754

EP - 1760

JO - Computational Mathematics and Mathematical Physics

JF - Computational Mathematics and Mathematical Physics

SN - 0965-5425

IS - 11

ER -

ID: 71957750