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# Approximation of time-dependent viscoelastic fluid flows with the Lagrange-Galerkin method

2 IDOPT - System identification and optimization in physics and environment
Inria Grenoble - Rhône-Alpes, CNRS - Centre National de la Recherche Scientifique : UMR5527
Abstract : 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.
Document type :
Journal articles

Cited literature [30 references]

https://hal.inria.fr/inria-00000345
Contributor : Pierre Saramito Connect in order to contact the contributor
Submitted on : Monday, September 26, 2005 - 2:50:12 PM
Last modification on : Friday, February 4, 2022 - 3:34:03 AM
Long-term archiving on: : Thursday, April 1, 2010 - 9:01:24 PM

### Identifiers

• HAL Id : inria-00000345, version 1

### Citation

Mohammed Bensaada, Driss Esselaoui, Pierre Saramito. Approximation of time-dependent viscoelastic fluid flows with the Lagrange-Galerkin method. Numerische Mathematik, Springer Verlag, 2005. ⟨inria-00000345⟩

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