伪双曲方程一个非协调混合元方法超收敛分析

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

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.

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 post-processing technique,the su-perclose properties and superconvergence results with order O（h2） for the primitive solution in Hx -norm and the inter-mediate variable in L2 -norm were deduced separately for semi-discrete scheme. At the same time,the superclose prop-erties with order O（h2＋τ2） and optimal order error estimates with order O（h＋τ2） of original variable in tf1 -norm and intermediate variable in L2 -norm were separately derived for a second order fully- discrete scheme.