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.

    Author(s):Barrenechea, Gabriel R. ORCID logoORCID: https://orcid.org/0000-0003-4490-678X, Castillo, Ernesto and Codina, Ramon
    Item type:Article
    ID code:64030
    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:17 Nov 2019 01:47
    Related URLs:
    URI:https://strathprints.strath.ac.uk/id/eprint/64030
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