Stable finite element methods for the Stokes problem

Yongdeok Kim, Sungyun Lee
2000 International Journal of Mathematics and Mathematical Sciences  
The mixed finite element scheme of the Stokes problem with pressure stabilization is analyzed for the cross-gridPk−Pk−1elements,k≥1, using discontinuous pressures. ThePk+−Pk−1elements are also analyzed. We prove the stability of the scheme using the macroelement technique. The order of convergence follows from the standard theory of mixed methods. The macroelement technique can also be applicable to the stability analysis for some higher order methods using continuous pressures such as
more » ... es such as Taylor-Hood methods, cross-grid methods, or iso-grid methods.
doi:10.1155/s0161171200002908 fatcat:lv3lw6lv4zhbhimyfkmaq76d3i