四阶强阻尼波动方程新混合元模式的高精度分析

High Accuracy Analysis of a New Mixed Finite Element Model for Fourth-order Strongly Damped Wave Equations

本文针对四阶强阻尼波动方程研究一种新混合元逼近格式.基于双线性元Q11及其梯度空间Q01×Q10的高精度分析,并借助于插值后处理技术,在半离散和全离散格式下,分别导出原始变量u在H1模和中间变量p珝在L2模意义下相应的超逼近性质及超收敛结果.

In this paper,a new mixed finite element approximate formulation is studied for fourth-order strongly damped wave equations. Based on high accuracy analysis of the bilinear finite element Q11 and its gradient space Q01×Q10, along with the interpolation post-process- ing technique, the corresponding superclose properties and the global superconvergence re- sults of original variable u in H1 -norm and intermediate variable p→ in L2 -norm are drived for the semi-discrete and fully-discrete scheme.