强阻尼波动方程的非协调混合有限元分析

摘要：

研究了非线性强阻尼波动方程的E1Qrot+Q10×Q01非协调混合有限元方法.利用该单元的高精度分析,借助于E1Qrot元所具有的两个性质:(a)其相容误差为O(h2)阶比它的插值误差高一阶;(b)插值算子与Ritz投影等价,以及插值后处理技术,在半离散的格式下分别导出了原始变量u的H1模和流量的L2模下O(h2)阶超逼近;整体超收敛性质.最后,通过构造一个新的全离散格式,得到了O(h2+τ2)的超逼近结果.

In this paper,with help of E_1（Qrot）＋Q_（10）×Q_（01）element,a nonconforming mixed finite element method for nonlinear strongly damped wave Equation is investigated By utilizing high accuracy analysis,two special properties of E_1（Qrot）element：（a）the consistency error is of order O（h2）which is one order higher than its interpolation error;（b）the interpolation operator is equivalent to its Ritz-projection operator,the super-close and the global super-convergence results with order O（h2）for the primitive solution u in broken H1-norm and flux variable  in L2-norm are obtained through interpolated postprocessing approach,respectively for semi-discrete scheme.At the same time,the super-close results with order O（h2＋τ2）are obtained through constructing a new full-discrete scheme.

作者:

毛凤梅 刁群

机构地区:

平顶山学院数学与统计学院

出处:

《betway官方app 学报：自然科学版》 CAS 北大核心 2016年第2期22-28,共7页

基金:

国家自然科学基金(11271340) 河南省科技计划项目(162300410082)

关键词:

非线性强阻尼波动方程 非协调混合元 半离散和全离散格式 超逼近 超收敛

strongly damped wave equations nonconforming mixed element semi-discrete full-discrete schemes super-close super-convergence

分类号:

O242.21 [理学—计算数学]

强阻尼波动方程的非协调混合有限元分析.pdf