W1,q stability of the Fortin operator for the MAC scheme
Résumé
We prove in this paper the continuity of the natural pro- jection operator from W1,q(Ω)d to the MAC discrete space of piece- 0 wise constant functions over the dual cells, endowed with the finite volume W1,q-discrete norm. Since this projection operator is also a Fortin operator (that is an operator which "preserves" the diver- gence), this result may be applied to control the pressure in mixed problems where the test function for the velocity must be more reg- ular than usual (i.e. more regular than H01(Ω)d).
Domaines
Analyse numérique [math.NA]
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