Superconvergence analysis and extrapolation of bilinear finite element for Schrdinger equation

The bilinear finite element approximation is mainly discussed for Schrdinger equation. The superclose property with O (h2) order is obtained in H1-norm by use of the derivative transfering skill and the high accuracy results of the element. Also,the global superconvergence result is given in H1-norm through the interpolation post-processing technique. Furthermore,through constructing a new extrapolation scheme,the extrapolation solution with O( h3) order is deduced which is two order higher than the traditional error estimate.