非线性伪双曲方程的类Carey元高精度分析

研究了非协调类Carey元对非线性伪双曲方程的Galerkin逼近.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,平均值技巧和插值后处理技术,在抛弃传统的Ritz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和整体超收敛结果.同时,针对方程中系数为线性的情形建立一个具有二阶精度的全离散逼近格式,导出了相应的超逼近和超收敛结果.

High Accuracy Analysis of Quasi-Carey Element for Nonlinear Pseudo-hyperbolic Equations

The Galerkin finite element mothed for nonlinear pseudo-hyperbolic equations with nonconforming quasi-Carey element is studied.Based on the special property of the element(i.e.the consistency error is one order higher than its interpolation error in the energy norm)and high accuracy analysis result of the linear triangular element,the superclose property and global superconvergence result in energy norm with order O(h2)for semi-discrete scheme are obtained employing the mean-value technique and interpolated postprocessing approach.At the same time,a second order fully-discrete scheme is established for quasi-linear case.The corresponding superclose property and superconvergence result of order O(h2+τ2)are deduced.Here,h andτare parameters of subdivision in space and time step respectively.