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.
Original language | English |
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Pages (from-to) | 792–819 |
Number of pages | 28 |
Journal | IMA Journal of Numerical Analysis |
Volume | 39 |
Issue number | 2 |
Early online date | 24 Apr 2018 |
DOIs | |
Publication status | Published - 1 Apr 2019 |
Keywords
- viscoelastic fluids
- stabilised finite element methods
- time-dependent flows