Unconditional error estimates for time dependent viscoelastic fluid flow

Haibiao Zheng; Jiaping Yu; Li Shan

doi:10.1016/j.apnum.2017.03.010

Unconditional error estimates for time dependent viscoelastic fluid flow

Haibiao Zheng, Jiaping Yu, Li Shan

School of Mathematical Sciences

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

18 Scopus citations

Abstract

The unconditional convergence of finite element method for two-dimensional time-dependent viscoelastic flow with an Oldroyd B constitutive equation is given in this paper, while all previous works require certain time-step restrictions. The approximation is stabilized by using the Discontinuous Galerkin (DG) approximation for the constitutive equation. The analysis bases on a splitting of the error into two parts: the error from the time discretization of the PDEs and the error from the finite element approximation of corresponding iterated time-discrete PDEs. The approach used in this paper can be applied to more general couple nonlinear parabolic and hyperbolic systems.

Original language	English
Pages (from-to)	1-17
Number of pages	17
Journal	Applied Numerical Mathematics
Volume	119
DOIs	https://doi.org/10.1016/j.apnum.2017.03.010
State	Published - 1 Sep 2017

Keywords

DG method
Unconditional convergence
Viscoelastic fluid

Access to Document

10.1016/j.apnum.2017.03.010

Cite this

@article{ed2260b1c2e2445ea1f19f4fb9e985e5,

title = "Unconditional error estimates for time dependent viscoelastic fluid flow",

abstract = "The unconditional convergence of finite element method for two-dimensional time-dependent viscoelastic flow with an Oldroyd B constitutive equation is given in this paper, while all previous works require certain time-step restrictions. The approximation is stabilized by using the Discontinuous Galerkin (DG) approximation for the constitutive equation. The analysis bases on a splitting of the error into two parts: the error from the time discretization of the PDEs and the error from the finite element approximation of corresponding iterated time-discrete PDEs. The approach used in this paper can be applied to more general couple nonlinear parabolic and hyperbolic systems.",

keywords = "DG method, Unconditional convergence, Viscoelastic fluid",

author = "Haibiao Zheng and Jiaping Yu and Li Shan",

note = "Publisher Copyright: {\textcopyright} 2017",

year = "2017",

month = sep,

day = "1",

doi = "10.1016/j.apnum.2017.03.010",

language = "英语",

volume = "119",

pages = "1--17",

journal = "Applied Numerical Mathematics",

issn = "0168-9274",

publisher = "Elsevier B.V.",

}

TY - JOUR

T1 - Unconditional error estimates for time dependent viscoelastic fluid flow

AU - Zheng, Haibiao

AU - Yu, Jiaping

AU - Shan, Li

PY - 2017/9/1

Y1 - 2017/9/1

N2 - The unconditional convergence of finite element method for two-dimensional time-dependent viscoelastic flow with an Oldroyd B constitutive equation is given in this paper, while all previous works require certain time-step restrictions. The approximation is stabilized by using the Discontinuous Galerkin (DG) approximation for the constitutive equation. The analysis bases on a splitting of the error into two parts: the error from the time discretization of the PDEs and the error from the finite element approximation of corresponding iterated time-discrete PDEs. The approach used in this paper can be applied to more general couple nonlinear parabolic and hyperbolic systems.

AB - The unconditional convergence of finite element method for two-dimensional time-dependent viscoelastic flow with an Oldroyd B constitutive equation is given in this paper, while all previous works require certain time-step restrictions. The approximation is stabilized by using the Discontinuous Galerkin (DG) approximation for the constitutive equation. The analysis bases on a splitting of the error into two parts: the error from the time discretization of the PDEs and the error from the finite element approximation of corresponding iterated time-discrete PDEs. The approach used in this paper can be applied to more general couple nonlinear parabolic and hyperbolic systems.

KW - DG method

KW - Unconditional convergence

KW - Viscoelastic fluid

UR - https://www.scopus.com/pages/publications/85016499921

U2 - 10.1016/j.apnum.2017.03.010

DO - 10.1016/j.apnum.2017.03.010

M3 - 文章

AN - SCOPUS:85016499921

SN - 0168-9274

VL - 119

SP - 1

EP - 17

JO - Applied Numerical Mathematics

JF - Applied Numerical Mathematics

ER -

Unconditional error estimates for time dependent viscoelastic fluid flow

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this