Analysis of a stabilised finite element method for power-law fluids

Barrenechea, Gabriel R. and Süli, Endre (2023) Analysis of a stabilised finite element method for power-law fluids. Constructive Approximation, 57 (2). pp. 295-325. ISSN 0176-4276 (https://doi.org/10.1007/s00365-022-09591-4)

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Abstract

A low-order finite element method is constructed and analysed for an incompressible non-Newtonian flow problem with power-law rheology. The method is based on a continuous piecewise linear approximation of the velocity field and piecewise constant approximation of the pressure. Stabilisation, in the form of pressure jumps, is added to the formulation to compensate for the failure of the inf-sup condition, and using an appropriate lifting of the pressure jumps a divergence-free approximation to the velocity field is built and included in the discretisation of the convection term. This construction allows us to prove the convergence of the resulting finite element method for the entire range r>2dd+2 of the power-law index r for which weak solutions to the model are known to exist in d space dimensions, d∈ { 2 , 3 }.

ORCID iDs

Barrenechea, Gabriel R. ORCID logoORCID: https://orcid.org/0000-0003-4490-678X and Süli, Endre;
  • Item type:Article
    ID code:82848
    Dates:
    Date
    Event
    30 April 2023
    Published
    13 October 2022
    Published Online
    28 August 2022
    Accepted
    Subjects:Science > Mathematics
    Department:Faculty of Science > Mathematics and Statistics
    Depositing user: Pure Administrator
    Date deposited:20 Oct 2022 10:30
    Last modified:11 Nov 2024 13:40
    URI:https://strathprints.strath.ac.uk/id/eprint/82848
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