中文摘要：

本文利用广义差分法讨论了二维粘弹性问题．建立了二维粘弹性问题的广义差分格式，给出了一种新的初始值近似，证明了广义差分解的最优L^p计和W^l,p（2≤p≤∞）模估计，同时得到了广义的Ritz-Volterra投影和广义差分解之间的超收敛的W^l,p（2≤p≤∞）模的误差估计．最后给出了一个数值算例以验证该方法的可行性．

英文摘要：

In this paper, generalized difference methods（GDM） for two-dimensional viscoelastic problems are proposed and analyzed. The special initial values are given in the generalized difference scheme, so we obtain optimal error estimates in L^p and W^l,P（2≤_ p≤ ∞） as well as some superconvergence estimates in W^l,p（2≤ p ≤∞） between the GDM solution and the generalized Ritz-Volterra projection of the exact solution. And finally, a numerical example is given.