伪抛物型积分微分方程一个新的混合有限元分析

A New Mixed Finite Element Analysis for Pseudo-parabolic Intergo-differential Equation

【目的】研究伪抛物型积分微分方程一个新的混合元模式。【方法】利用Bramble-Hilbert引理,对不完全双二次元Q-2及其梯度空间进行探索。【结果】证明了单元具有的一个新的高精度理论。【结论】在半离散和向后欧拉全离散格式下,分别导出了原始变量u在H^1-模和中间变量p在L^2-模意义下的超逼近性质。

[Purposes]A new mixed finite element pattern for pseudo-parabolic intergo-differential equation is studied.[Methods]Though Bramble-Hilbert lemma,the spaces of incomplete biquadratic element Q-2 and its gradient are explored.[Findings]A new high precision theory on element is proved.[Conclusions]The superclose properties for the primitive variable uin H^1-norm and the intermediate variable pin L^2-norm are obtained respectively for semi-discrete and the backward Euler fully discrete schemes.