Lp and W1,p Error Estimates for First Order GDM on One-Dimensional Elliptic and Parabolic Problems

• Gong, Jing (Department of Mathematics Shandong Normal University) ;
• Li, Qian (Department of Mathematics Shandong Normal University)
• Published : 2000.12.31

Abstract

In this paper, we consider first order generalized difference scheme for the two-point boundary value problem and one-dimensional second order parabolic type problem. The optimal error estimates in $L_p$ and $W^{1,p}$ ($2{\leq}p{\leq}{\infty}$) as well as some superconvergence estimates in $W^{1,p}$ ($2{\leq}p{\leq}{\infty}$) are obtained. The main results in this paper perfect the theory of GDM.