有限元解的梯度佳点

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The Optimal Point of the Gradient of Finite Element Solution

摘要: 我们考虑二阶椭圆方程的第一边值问题及奇妙族矩形元。文[2,3,9]证明了有限元解的梯度在高斯点具有超收敛性。本文假定椭圆方程的系数在有界区域Ω中曲线S上有第一类间断,在此意义下推广了文[2,3,9]。

Abstract: We consider the first boundary value problem of the second order elliptic equation and serendipity rectangular elements. Papers [2,3,9] proved that the gradients of finite element solution possess superconvergence at Gaussianpoint. In this paper, we extend the results in papers [2,3,9] in the sense that the coefficients of the elliptic equations are discontinuous on a curve S which lies in the bounded domain Ω.

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