Approximation of time-dependent viscoelastic fluid flows with the Lagrange-Galerkin method
Résumé
An optimal {\em a priori} error estimate ${\cal O}\left(h^{k}+\Delta t\right)$, result is presented for viscoelastic fluid flow problems in $\bbfR^d$, $d=2,3$ when using a suitable Lagrange-Galerkin method, under the constraint $\Delta t \leq h^{d/2+\varepsilon}$ for the time step $\Delta t$ and the mesh size $h$. The time discretization bases on a backward-Euler scheme together with a specific approximation of the Oldroyd derivative of tensors. A mixed stress-velocity-pressure $(P_{k-1},P_k,P_{k-1})$ finite element method is used for the space discretization. This approach leads to a fully decoupled algorithm that is of practical interest, both for continuous and discontinuous approximations of stresses.
Domaines
Analyse numérique [math.NA]
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