Time-dependent semi-discrete analysis of the viscoelastic fluid flow problem using a variational multiscale stabilised formulation

Gabriel R. Barrenechea, Ernesto Castillo, Ramon Codina

Research output: Contribution to journal › Article

Abstract

In this article we analyse a stabilised finite element formulation recently proposed to approximate viscoelastic fluid flows. The formulation has shown to have accuracy and robustness in the different benchmarks tested in the viscoelastic framework and permitting the use of equal interpolation of the unknown fields. We first present results about a linearised sub-problem, for which well-posedness and stability results can be proved. Then, the semi-discrete nonlinear time-dependent case is addressed using a fixed point theorem, which allows us to prove existence of a semi-discrete solution, along with error estimates.
LanguageEnglish
Number of pages28
JournalIMA Journal of Numerical Analysis
Early online date24 Apr 2018
DOIs
Publication statusE-pub ahead of print - 24 Apr 2018

Fingerprint

Viscoelastic Flow
Viscoelastic Fluid
Fluid Flow
Flow of fluids
Interpolation
Stabilized Finite Elements
Formulation
Well-posedness
Fixed point theorem
Error Estimates
Interpolate
Benchmark
Robustness
Unknown
Framework

Keywords

  • viscoelastic fluids
  • stabilised finite element methods
  • time-dependent flows

Cite this

Barrenechea, Gabriel R. ; Castillo, Ernesto ; Codina, Ramon. / Time-dependent semi-discrete analysis of the viscoelastic fluid flow problem using a variational multiscale stabilised formulation. In: IMA Journal of Numerical Analysis. 2018.
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Barrenechea, GR, Castillo, E & Codina, R 2018, 'Time-dependent semi-discrete analysis of the viscoelastic fluid flow problem using a variational multiscale stabilised formulation' IMA Journal of Numerical Analysis. https://doi.org/10.1093/imanum/dry018

Time-dependent semi-discrete analysis of the viscoelastic fluid flow problem using a variational multiscale stabilised formulation. / Barrenechea, Gabriel R.; Castillo, Ernesto; Codina, Ramon.

In: IMA Journal of Numerical Analysis, 24.04.2018.

Research output: Contribution to journal › Article

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AU - Castillo, Ernesto

AU - Codina, Ramon

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N2 - In this article we analyse a stabilised finite element formulation recently proposed to approximate viscoelastic fluid flows. The formulation has shown to have accuracy and robustness in the different benchmarks tested in the viscoelastic framework and permitting the use of equal interpolation of the unknown fields. We first present results about a linearised sub-problem, for which well-posedness and stability results can be proved. Then, the semi-discrete nonlinear time-dependent case is addressed using a fixed point theorem, which allows us to prove existence of a semi-discrete solution, along with error estimates.

AB - In this article we analyse a stabilised finite element formulation recently proposed to approximate viscoelastic fluid flows. The formulation has shown to have accuracy and robustness in the different benchmarks tested in the viscoelastic framework and permitting the use of equal interpolation of the unknown fields. We first present results about a linearised sub-problem, for which well-posedness and stability results can be proved. Then, the semi-discrete nonlinear time-dependent case is addressed using a fixed point theorem, which allows us to prove existence of a semi-discrete solution, along with error estimates.

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Barrenechea GR, Castillo E, Codina R. Time-dependent semi-discrete analysis of the viscoelastic fluid flow problem using a variational multiscale stabilised formulation. IMA Journal of Numerical Analysis. 2018 Apr 24. https://doi.org/10.1093/imanum/dry018

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