非线性伪双曲积分微分方程的类Carey元超收敛分析

Superconvergence Analysis of Quasi-carey Element for Nonlinear Pseudo-hyperbolic Integro-differential Equations

将非协调三角形类Carey元应用于非线性伪双曲积分微分方程进行了超收敛分析.利用该元在能量模意义下非协调误差比插值误差高一阶的特殊性质,线性三角形元的高精度分析结果及平均值技巧,在抛弃传统的Ritz-Volterra投影的情形下,得到了半离散格式能量模意义下的超逼近性质.进一步地,借助插值后处理技术,导出了相应的整体超收敛结果.

The superconvergence analysis for nonlinear pseudo-hyperbolic integro-differential equations by using nonconforming triangular quasi-Carey element is studied.With the help of the special property of the element,that is,the consistency error is one order higher than its interpolation error in the energy norm,the high accuracy analysis result of the linear triangular element and mean-value technique,the superclose properties in energy norm for semi-discrete scheme are obtained,without requiring the traditional Ritz-Volterra projection operator.Furthermore,by employing interpolated postprocessing approach,the corresponding superconvergence result is deduced.