伪双曲方程一个非协调混合元方法超收敛分析

基于非协调EQrot1元和零阶R-T元针对伪双曲方程,建立了一个自然满足B-B条件的非协调低阶混合元逼近格式.借助单元插值算子的特殊性质、导数转移技巧和插值后处理技术,在半离散格式下给出了原始变量在H1-模和中间变量在L2-模意义下的O(h2)阶超逼近性与整体超收敛结果.同时,对于一个二阶全离散格式得到了原始变量H1-模的O(h2+τ2)超逼近性和中间变量L2-模的O(h+τ2)最优误差估计.

Superconvergence Analysis of a Nonconforming Mixed Finite Element Method for Pseudo-hyperbolic Equation

With help of the nonconforming EQrot1 element and zero order Raviart-Thomas element,a new low order nonconforming mixed finite elements approximation scheme was proposed for the pseudo-hyperbolic equation,which can satisfy Brezzi-Babuska condition automatically.Based on the special characters of the interpolation operators of the elements,derivative transferring technique with respect to the time and interpolation postprocessing technique,the superclose properties and superconvergence results with order O(h2)for the primitive solution in H1-norm and the intermediate variable in L2-norm were deduced separately for semi-discrete scheme.At the same time,the superclose properties with order O(h2+τ2)and optimal order error estimates with order O(h+τ2)of original variable in H1-norm and intermediate variable in L2-norm were separately derived for a second order fully-discrete scheme.