A standard method for proving the inf-sup condition implying stability of finite element approximations for the stationary Stokes equations is to construct a Fortin operator. In this paper, we show how this can be done for two-dimensional triangular and rectangular Taylor-Hood methods, which use continuous piecewise polynomial approximations for both velocity and pressure.
@article{M2AN_2008__42_3_411_0, author = {Falk, Richard S.}, title = {A {Fortin} operator for two-dimensional {Taylor-Hood} elements}, journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique}, pages = {411--424}, publisher = {EDP-Sciences}, volume = {42}, number = {3}, year = {2008}, doi = {10.1051/m2an:2008008}, mrnumber = {2423792}, zbl = {1143.65085}, language = {en}, url = {http://www.numdam.org/articles/10.1051/m2an:2008008/} }
TY - JOUR AU - Falk, Richard S. TI - A Fortin operator for two-dimensional Taylor-Hood elements JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2008 SP - 411 EP - 424 VL - 42 IS - 3 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an:2008008/ DO - 10.1051/m2an:2008008 LA - en ID - M2AN_2008__42_3_411_0 ER -
%0 Journal Article %A Falk, Richard S. %T A Fortin operator for two-dimensional Taylor-Hood elements %J ESAIM: Modélisation mathématique et analyse numérique %D 2008 %P 411-424 %V 42 %N 3 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an:2008008/ %R 10.1051/m2an:2008008 %G en %F M2AN_2008__42_3_411_0
Falk, Richard S. A Fortin operator for two-dimensional Taylor-Hood elements. ESAIM: Modélisation mathématique et analyse numérique, Volume 42 (2008) no. 3, pp. 411-424. doi : 10.1051/m2an:2008008. http://www.numdam.org/articles/10.1051/m2an:2008008/
[1] Error estimates for finite element solution of the Stokes problem in the primitive variables. Numer. Math. 33 (1979) 211-224. | MR | Zbl
and ,[2] Stability of higher-order triangular Hood-Taylor methods for the stationary Stokes equation. Math. Models Methods Appl. Sci. 4 (1994) 223-235. | MR | Zbl
,[3] Three-dimensional finite element methods for the Stokes problem. SIAM J. Numer. Anal. 34 (1997) 664-670. | MR | Zbl
,[4] Stability of higher-order Hood-Taylor methods. SIAM J. Numer. Anal. 28 (1991) 581-590. | MR | Zbl
and ,[5] Mixed and hybrid finite element methods. Springer-Verlag, New York (1991). | MR | Zbl
and ,[6] Finite Element Methods for Navier-Stokes equations: theory and algorithms, Springer Series in Computational Mathematics 5. Springer-Verlag, Berlin (1986). | MR | Zbl
and ,[7] Norm estimates for a maximal right inverse of the divergence operator in spaces of piecewise polynomials. RAIRO Modél. Math. Anal. Numér. 19 (1985) 111-143. | Numdam | MR | Zbl
and ,[8] Error analysis of some finite element methods for the Stokes problem. Math. Comp. 54 (1990) 494-548. | MR | Zbl
,[9] Error estimates for a mixed finite element approximation of the Stokes equations. RAIRO Anal. Numér. 18 (1984) 175-182. | Numdam | MR | Zbl
,Cited by Sources: