%0 Journal Article
%T W1,q stability of the Fortin operator for the MAC scheme
%+ Laboratoire d'Analyse, Topologie, Probabilités (LATP)
%+ Institut de Radioprotection et de Sûreté Nucléaire (IRSN)
%A Gallouët, Thierry
%A Herbin, Raphaele
%A Latché, Jean-Claude
%< avec comité de lecture
%@ 0008-0624
%J Calcolo
%I Springer Verlag
%V 49
%N 1
%P 63-71
%8 2012-02-24
%D 2012
%R 10.1007/s10092-011-0045-x
%K MAC scheme
%K Projection stability
%K Fortin operator
%Z 65M12, 76D07, 76M12
%Z Mathematics [math]/Numerical Analysis [math.NA]Journal articles
%X 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).
%G English
%2 https://hal.science/hal-00673682/document
%2 https://hal.science/hal-00673682/file/fortin-mac-10.pdf
%L hal-00673682
%U https://hal.science/hal-00673682
%~ IRSN
%~ LATP
%~ CNRS
%~ UNIV-AMU
%~ EC-MARSEILLE
%~ I2M
%~ TDS-MACS