On the convergence of Variational multiscale methods based on Newton's iteration for the incompressible flows

Feng Shi; Haibiao Zheng; Jiaping Yu; Ying Li

doi:10.1016/j.apm.2014.04.049

On the convergence of Variational multiscale methods based on Newton's iteration for the incompressible flows

Feng Shi
, Haibiao Zheng^*
, Jiaping Yu
, Ying Li

^*Corresponding author for this work

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

8 Scopus citations

Abstract

In this paper, the convergence of a general algorithm with θ-type stabilization form for the variational multiscale (VMS) method is presented. Meanwhile, explicit-type and implicit-type algorithms with linear convergence and quadratic convergence are derived from the θ-type algorithm, respectively. The combination of explicit-type and implicit-type algorithms are applied to adaptive VMS, which shows good efficiency. Finally, some numerical tests are shown to support the convergence analysis.

Original language	English
Pages (from-to)	5726-5742
Number of pages	17
Journal	Applied Mathematical Modelling
Volume	38
Issue number	23
DOIs	https://doi.org/10.1016/j.apm.2014.04.049
State	Published - 1 Dec 2014
Externally published	Yes

Keywords

Linear convergence
Navier-Stokes equations
Newton's iteration
Quadratic convergence
Variational multiscale method

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10.1016/j.apm.2014.04.049

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title = "On the convergence of Variational multiscale methods based on Newton's iteration for the incompressible flows",

abstract = "In this paper, the convergence of a general algorithm with θ-type stabilization form for the variational multiscale (VMS) method is presented. Meanwhile, explicit-type and implicit-type algorithms with linear convergence and quadratic convergence are derived from the θ-type algorithm, respectively. The combination of explicit-type and implicit-type algorithms are applied to adaptive VMS, which shows good efficiency. Finally, some numerical tests are shown to support the convergence analysis.",

keywords = "Linear convergence, Navier-Stokes equations, Newton's iteration, Quadratic convergence, Variational multiscale method",

author = "Feng Shi and Haibiao Zheng and Jiaping Yu and Ying Li",

note = "Publisher Copyright: {\textcopyright} 2014 Elsevier Inc.",

year = "2014",

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T1 - On the convergence of Variational multiscale methods based on Newton's iteration for the incompressible flows

AU - Shi, Feng

AU - Zheng, Haibiao

AU - Yu, Jiaping

AU - Li, Ying

PY - 2014/12/1

Y1 - 2014/12/1

N2 - In this paper, the convergence of a general algorithm with θ-type stabilization form for the variational multiscale (VMS) method is presented. Meanwhile, explicit-type and implicit-type algorithms with linear convergence and quadratic convergence are derived from the θ-type algorithm, respectively. The combination of explicit-type and implicit-type algorithms are applied to adaptive VMS, which shows good efficiency. Finally, some numerical tests are shown to support the convergence analysis.

AB - In this paper, the convergence of a general algorithm with θ-type stabilization form for the variational multiscale (VMS) method is presented. Meanwhile, explicit-type and implicit-type algorithms with linear convergence and quadratic convergence are derived from the θ-type algorithm, respectively. The combination of explicit-type and implicit-type algorithms are applied to adaptive VMS, which shows good efficiency. Finally, some numerical tests are shown to support the convergence analysis.

KW - Linear convergence

KW - Navier-Stokes equations

KW - Newton's iteration

KW - Quadratic convergence

KW - Variational multiscale method

UR - https://www.scopus.com/pages/publications/84921999758

U2 - 10.1016/j.apm.2014.04.049

DO - 10.1016/j.apm.2014.04.049

M3 - 文章

AN - SCOPUS:84921999758

SN - 0307-904X

VL - 38

SP - 5726

EP - 5742

JO - Applied Mathematical Modelling

JF - Applied Mathematical Modelling

IS - 23

ER -

On the convergence of Variational multiscale methods based on Newton's iteration for the incompressible flows

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Keywords

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