伪双曲方程一个非协调混合元方法超收敛分析

马戈; 胡双年

doi:10.3969/j.issn.1003-0972.2018.01.005

伪双曲方程一个非协调混合元方法超收敛分析

马戈,
胡双年

南阳理工学院数学与统计学院, 河南南阳 473004

基金项目:

国家自然科学基金项目（11671369）；河南省高等学校重点科研项目（17A110010）

详细信息

作者简介:
马戈(1964-),男,河南邓州人,教授,主要从事有限元方法与应用研究.

中图分类号: O242.21
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出版历程
- 收稿日期: 2017-09-05
- 修回日期: 2017-12-08
- 发布日期: 2018-01-09

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

School of Mathematics and Statistics, Nanyang Institute of Technology, Nanyang 473004, China

摘要

摘要: 基于非协调EQ₁^rot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.
- 伪双曲方程 /
- 非协调混合有限元 /
- 半离散和全离散 /
- 超逼近和超收敛
Abstract: With help of the nonconforming EQ₁^rot 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 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.
- pseudo-hyperbolic equation /
- nonconforming mixed finite element /
- semi-discrete and fully-discrete schemes /
- superclose properties and superconvergence

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参考文献(15)

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