抛物方程的非协调类Wilson元超收敛性分析和外推

Superconvergece analysis and extrapolation of nonconforining quasi-Wilson element for parabolic equations

本文主要研究类Wilson元对抛物方程的逼近,当问题的解υ∈H^3(Ω)及υ∈H^4(Ω)时,利用该元的非协调误差在能量模意义下分别可以达到O(h^2)和O(h^3)比其插值误差高一阶这一特殊性质,运用对时间t的导数转移技巧,再结合双线性元的高精度分析及插值后处理技术,导出了O(h^2)阶超逼近性质和整体超收敛,进一步地,通过构造了一个新的外推格式,得到了具有更高精度O(h^3)阶的外推结果。

In this paper, quasi-Wilson finite element approximation is mainly studied for parabolic equations. By using the special property of the element, that is, consistency error with order O（h2） or O（h3） （when u belongs to H3（Ω） or H4（Ω） in broken energy norm can be estimated to be one order higher than its interpolation error, the transformation of the derivative with respect to time t, the known higher accuracy analysis of bilinear finite element and post-processing technique, the superclose property and superconvergence with order O（h2） are derived. Furthermore, the extrapolation result with higher order O（h3） is obtained through constructing a new extrapolation scheme.