抛物积分微分方程非协调类Wilson元的整体超收敛和外推

GLOBAL SUPERCONVERGENCE AND EXTRAPOLATION OF QUASI-WILSON ELEMENT SOLUTION TO INTEGRO-DIFFERENTIAL OF PARABOLIC EQUATIONS

本文研究了类Wilson元对抛物积分微分方程的逼近的问题.利用当u∈H3()/H4()时,该元的非协调误差在能量模意义下可以达到O(h2)/O(h3)这一性质,并运用对时间t的导数转移技巧,结合双线性元的高精度结果及插值后处理技术,获得了O(h2)阶的超逼近和整体超收敛结果,最后,通过构造新的合适的外推格式,得到了具有更高精度O(h3)阶的近似解.

In this paper, quasi-Wilson finite element approximation is studied for integro- differential parabolic equations. By using the special character of the element,that is, the consistency error can be estimated with order O（h 2 ）/ O（h 3 ） when u belongs to H 3 （ ）/H 4 （ ） in energy norm, the transformation of the derivative with respect to time t, the known high accuracy analysis of bilinear finite element and postprocessing technique, the superclose property and global superconvergence to order O（h 2 ） are derived. Finally, the higher approximation solution to order O（h 3 ） is obtained through constructing a new suitable extrapolation scheme.