Estimation of Two Error Components in the Numerical Solution to the Problem of Nonisothermal Flow of Polymer Fluid between Two Coaxial Cylinders

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Estimation of Two Error Components in the Numerical Solution to the Problem of Nonisothermal Flow of Polymer Fluid between Two Coaxial Cylinders. / Blokhin, A. M.; Kruglova, E. A.; Semisalov, B. V.

In: Computational Mathematics and Mathematical Physics, Vol. 58, No. 7, 01.07.2018, p. 1099-1115.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{f049a7c4bf374f07bf7a57b9a92519b3,

title = "Estimation of Two Error Components in the Numerical Solution to the Problem of Nonisothermal Flow of Polymer Fluid between Two Coaxial Cylinders",

abstract = "An algorithm for solving a stationary nonlinear problem of a nonisothermal flow of an incompressible viscoelastic polymer fluid between two coaxial cylinders is developed on the basis of Chebyshev approximations and the collocation method. In test calculations, the absence of saturation of the algorithm is shown. A posteriori estimates of two error components in the numerical solution-the error of approximation method and the round-off error-are obtained. The behavior of these components as a function of the number of nodes in the spatial grid of the algorithm and the radius of the inner cylinder is analyzed. The calculations show exponential convergence, stability to rounding errors, and high time efficiency of the algorithm developed.",

keywords = "algorithm without saturation, Chebyshev polynomials, collocation method, error estimates, exponential convergence, polymer fluid dynamics",

author = "Blokhin, {A. M.} and Kruglova, {E. A.} and Semisalov, {B. V.}",

note = "Publisher Copyright: {\textcopyright} 2018, Pleiades Publishing, Ltd.",

year = "2018",

month = jul,

day = "1",

doi = "10.1134/S0965542518070035",

language = "English",

volume = "58",

pages = "1099--1115",

journal = "Computational Mathematics and Mathematical Physics",

issn = "0965-5425",

publisher = "PLEIADES PUBLISHING INC",

number = "7",

}

RIS

TY - JOUR

T1 - Estimation of Two Error Components in the Numerical Solution to the Problem of Nonisothermal Flow of Polymer Fluid between Two Coaxial Cylinders

AU - Blokhin, A. M.

AU - Kruglova, E. A.

AU - Semisalov, B. V.

PY - 2018/7/1

Y1 - 2018/7/1

N2 - An algorithm for solving a stationary nonlinear problem of a nonisothermal flow of an incompressible viscoelastic polymer fluid between two coaxial cylinders is developed on the basis of Chebyshev approximations and the collocation method. In test calculations, the absence of saturation of the algorithm is shown. A posteriori estimates of two error components in the numerical solution-the error of approximation method and the round-off error-are obtained. The behavior of these components as a function of the number of nodes in the spatial grid of the algorithm and the radius of the inner cylinder is analyzed. The calculations show exponential convergence, stability to rounding errors, and high time efficiency of the algorithm developed.

AB - An algorithm for solving a stationary nonlinear problem of a nonisothermal flow of an incompressible viscoelastic polymer fluid between two coaxial cylinders is developed on the basis of Chebyshev approximations and the collocation method. In test calculations, the absence of saturation of the algorithm is shown. A posteriori estimates of two error components in the numerical solution-the error of approximation method and the round-off error-are obtained. The behavior of these components as a function of the number of nodes in the spatial grid of the algorithm and the radius of the inner cylinder is analyzed. The calculations show exponential convergence, stability to rounding errors, and high time efficiency of the algorithm developed.

KW - algorithm without saturation

KW - Chebyshev polynomials

KW - collocation method

KW - error estimates

KW - exponential convergence

KW - polymer fluid dynamics

UR - http://www.scopus.com/inward/record.url?scp=85052233303&partnerID=8YFLogxK

U2 - 10.1134/S0965542518070035

DO - 10.1134/S0965542518070035

M3 - Article

AN - SCOPUS:85052233303

VL - 58

SP - 1099

EP - 1115

JO - Computational Mathematics and Mathematical Physics

JF - Computational Mathematics and Mathematical Physics

SN - 0965-5425

IS - 7

ER -

ID: 16265989