非线性抛物方程的EQ_1^(rot)非协调混合元方法的超收敛分析

Superconvergence Analysis of Nonlinear Parabolic Equation with the Nonconforming EQ_1^(rot) Mixed Finite Elements

基于EQ_1^(rot)非协调矩形元及零阶R-T元对非线性抛物方程构造了一个新的混合元格式.利用EQ_1^(rot)元所具有的两个特殊性质:(I)插值算子与其投影算子是一致的;(II)当所考虑问题的精确解属于H^3(ΩΩ)时,其相容误差可以达到O(h^2)(h是剖分参数),比插值误差高一阶.同时借助关于这两个单元的高精度分析、平均值技巧和插值后处理技术,得到了关于原始变量以及通量的超逼近和整体超收敛结果.

A new mixed finite elements scheme is proposed for nonlinear parabolic equation based on the nonconforming EQ1^rot element and zero orderR- Telement. By utilizing the two special properties of the EQ1^rot element： one is that the interpolation operator is identity to the traditional Ritz projection operator; another is that the consistency error is of orderO（h^2） （his the partition parameter） when the exact solution of the problem considered belongs to H^3 （Ω）, which is one order higher than the interpolation error. Furthermore, by utilizing the high accuracy analysis, means of the average value and interpolation post processing techniques, the superclose and superconvergence results of the original and flux variables are derived.