抄録
In this paper,we consider a collocation-H-1-Galerkin approximation for the elliptic boundary value problem of the form: Lu≡∇•(a∇u)+b•∇u+cu=f in Ω with u=0 on ∂Ω, where Ω is a rectangular domain in R2. The method uses tensor products of discontinuous piecewise polynomials as the trial spaces. Global L∞ error estimates of optimal order are established. Moreover, it is shown that the accuracy of the approximate solution at certain Gauss point is one order higher than the global,i. e., some superconvergence estimates are obtained. A numerical examaple which illustrates these results is presented.
