Abstract.
This paper deals with a posteriori estimates for the finite element solution of the Stokes problem in stream function and vorticity formulation. For two different discretizations, we propose error indicators and we prove estimates in order to compare them with the local error. In a second step, these results are extended to the Navier-Stokes equations.
Résumé
Cet article traite d'estimations a posteriori pour la résolution du problème de Stokes par éléments finis en formulation fonction courant et tourbillon. Pour deux discrétisations différentes, on propose des indicateurs d'erreur et on établit des estimations permettant de les comparer à l'erreur locale. Ces résultats sont ensuite étendus aux équations de Navier-Stokes.
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Received March 25, 1996 / Revised version received April 7, 1997
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Amara, M., Younes, M. & Bernardi, C. Error indicators for the Navier-Stokes equations in stream function and vorticity formulation. Numer. Math. 80, 181–206 (1998). https://doi.org/10.1007/s002110050365
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DOI: https://doi.org/10.1007/s002110050365