(untitled) (Journal of Computational Mathematics, 1989)
Recently, the Richardson extrapolation for the elliptic Ritz projection with linear triangular elements on a general convex polygonal domain was discussed by Lin and Lu. We go back in this note to the simplest case, i.e. the bilinear rectangular elements on a rectangular domain which is a parallel case of the one-triangle model in the early work of Lin and Liu. We find that the finite element argument for the Richardson extrapolation with an accuracy of O(h^4) needs only the regularity of H^4,∞ for the solution u but the finite difference argument for extrapolation with O(h^s+α) accuracy needs uC^5+α(0＜α＜1). Moreover, a formula is suggested to guarantee the extrapolation of O(h^4) accuracy at fine gridpoints as well as at coarse gridpoints.