一类非线性双曲积分微分方程的类Carey元超收敛和外推

Superconvergence and Extrapolation of Quasi-Carey Element for a Kind of Nonlinear Hyperbolic Integro-differential Equations

利用非协调三角形类Carey元对一类非线性双曲积分微分方程进行了超收敛分析和外推．基于单元的特殊性质，线性三角形元的高精度分析结果，平均值和导数转移技巧，以及插值后处理技术，得到了半离散格式能量模意义下具有O（h2）阶的超逼近性质和整体超收敛结果．同时，通过构造一个合适的辅助问题，运用Ri—chordson外推格式，导出了具有O（h4）阶的外推结果．

The superconvergence analysis and extrapolation for a kind of nonlinear hyperbolic integro-differential equations by using nonconforming triangular quasi-Carey element are studied. Based on the special properties of the elements, high accuracy analysis result of linear triangular element, mean-value and derivative transfering technique, interpolated postprocessing approach, the superclose properties and global superconvergence result with order O（h2） in energy norm for semi-discrete scheme are obtained. At the same time, by constructing a suitable auxiliary problem, the extrapolation result with order O（h4） is derived through Richardson extrapolation scheme.