一类双曲型积分微分问题有限元逼近的超收敛估计(英文)

Superconvergence of a Finite Element Method for a Kind of Hyperbolic Integro-differential Problems

本文研究双曲型积分微分方程的半离散有限元逼近格式的超收敛估计。基于一种新的初值近似,得到了有限元解与精确解的Ritz-Volterra投影的Ws,p(Ω)模的如下超收敛估计:k>1,s=0,2≤p≤∞时,超收敛1阶;k>1,s=1,2≤p<∞时,超收敛2阶;k>1,s=1,p=∞时,几乎超收敛2阶;k=1,s:1,2≤p≤∞时,超收敛1阶。

In this paper, we study the superconvergence of a semi-discrete finite element scheme for hyperbolic integro-differential problems using any degree of elements. The scheme is based on introducing a new way of approximating initial conditions. We obtain several superconvergence results for the error between the approximate solution and the Ritz Volterra projection of the exact solution. For k > 1, we obtain first order gain in Lp (2 ≤ p ≤ ∞) norm, second order in W1,p(2 ≤ p < ∞) norm and almost second order in W1,∞ norm. For k = 1, we obtain first order gain in W1,p (2 ≤ p ≤ ∞) norm.