Burgers方程的非协调特征有限元方法

A nonconforming characteristic finite element method for Burgers equations

给出了二维Burgers方程一个Crouzeix-Raviart型非协调特征有限元格式,利用有限元空间的特性,在不使用传统的投影算子的情况下,得到了H1模的最优误差估计及其超逼近性质,并通过构造插值后处理算子得到了超收敛结果。

A Crouzeix-Raviart type nonconforming characteristic finite element scheme is proposed for 2D Burgers equations.By use of some special properties of the finite element interpolation,and without the projection operator which is a vital tool in the conventional finite element convergence analysis of evolution equations,the optimal H1-norm error estimate and some superclose properties are obtained.Also,based on the interpolated postprocessing trick,the global superconvergence is derived.