Error estimates for a stabilized finite element method for the Oldroyd B model. (English) Zbl 1107.76043
Summary: We study a new approximation scheme of transient viscoelastic fluid flow obeying Oldroyd-B-type constitutive equation. The new stabilized formulation bases on the choice of a modified Euler method connected to the streamline upwinding Petrov-Galerkin method [the authors and D. Sandri, Numer. Methods Partial Differ. Equations 21, No. 1, 170–189 (2005; Zbl 1066.65092)], in order to stabilize the tensorial transport term of the Oldroyd derivative. Assuming that the continuous problem admits a sufficiently smooth and sufficiently small solution, we derive a priori error estimates for the approximation in terms of the mesh parameter \(h\) and time discretization parameter \(\Delta t\).
MSC:
| 76M10 | Finite element methods applied to problems in fluid mechanics |
| 76A10 | Viscoelastic fluids |
| 65M15 | Error bounds for initial value and initial-boundary value problems involving PDEs |
| 65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |
Citations:
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