非线性双曲方程的类Wilson元超收敛分析

Superconvergence Analysis of Quasi-Wilson Element for Nonlinear Hyperbolic Equation

在半离散格式下讨论了非线性双曲方程的类Wilson非协调有限元逼近.利用该元的相容误差在能量模意义下可以达到O(h2)比其插值误差高一阶的特殊性质,再结合其协调部分的高精度分析及导数转移和平均值技巧,导出了O(h2)阶的超逼近性.进而,通过运用插值后处理方法得到了超收敛结果.

Nonconforming quasi-Wilson finite element approximation to nonlinear hyperbolic equation is discussed for the semi-discrete scheme. By use of the special property of the element, i. e., the consistence error in energy norm is of order O（h2） , one order higher than its interpolation error, the superclose property with order O（h2） is derived by higher accuracy a- nalysis of its conforming part, the derivative transfering and mean-value technique. Furthermore, the superconvergence result is obtained through the interpolated postprocessing method.