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 journalArticle

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

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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

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