A refined mixed finite element method for the boussinesq equations in polygonal domains |
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| Authors: | Farhloul, M. Nicaise, S. Paquet, L. |
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| Affiliation: | 1 Université de Moncton, Département de Mathématiques et de Statistique, NB, E1A 3 E9, Moncton, Canada 2 Université de Valenciennes et du Hainaut Cambrésis, MACS, ISTV, BP 311, F-59304 Valenciennes Cedex, France 3 Université de Valenciennes et du Hainaut Cambrésis, MACS, ISTV, BP 311, F-59304 Valenciennes Cedex, France |
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| Abstract: | This paper deals with the mixed formulation of the Boussinesqequations in two-dimensional polygonal domains and its numericalapproximation. The steady solution has a singular behaviournear the corner points so that we show that it belongs to appropriateweighted Sobolev spaces. Since uniform meshes lead to a slowconvergence rate, we derive appropriate refinement rules onthe meshes near the corner points in order to restore the quasi-optimalrate of convergence. A numerical test is finally presented whichconfirms the theoretical convergence rates. Received 26 November 1999. Accepted 25 August 2000. |
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