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

Barrenechea, Gabriel R. and Castillo, Ernesto and Codina, Ramon (2019) Time-dependent semi-discrete analysis of the viscoelastic fluid flow problem using a variational multiscale stabilised formulation. IMA Journal of Numerical Analysis, 39 (2). 792–819. ISSN 0272-4979

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    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.

    ORCID iDs

    Barrenechea, Gabriel R. ORCID logoORCID: https://orcid.org/0000-0003-4490-678X, Castillo, Ernesto and Codina, Ramon;
    • Item type:Article
      ID code:64030
      Dates:
      Date
      Event
      1 April 2019
      Published
      24 April 2018
      Published Online
      6 March 2018
      Accepted
      Keywords:viscoelastic fluids, stabilised finite element methods, time-dependent flows, Mathematics, Mathematics(all)
      Subjects:Science > Mathematics
      Department:Faculty of Science > Mathematics and Statistics
      Depositing user: Pure Administrator
      Date deposited:14 May 2018 10:36
      Last modified:13 May 2021 01:17
      Related URLs:
      URI:https://strathprints.strath.ac.uk/id/eprint/64030
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