High Accury Analysis For Stokes Problems Under Anisotropic Meshes

Q₂ - P₁ mixed finite element method for Stokes problem on anisotropic meshes will be discussed in this paper. On the one hand, the same superclose properties as the traditional methods are derived through integral identity technique. At the same time, a pair postprocessing operators for velocity and pressure are constructed. Based on the interpolated postprocessing technique, and the former one has an anisotropic property. Thus the global superconvergence is obtained. On the other hand, the asymptotic error expansion and the extrapolation between the finite element solution and the exact solution of interpolation of Q₂ - P₁ mixed finite element method for Stokes problem are considered. The technique employed is to use integral identity techniques to detemine the main term of the error between the exact solution and its finite element interpolation, and then to derive one order higher convergence rate than the general error estimate by postprocessing technique and exptrapolation.