电报方程的H^1-Galerkin非协调混合有限元逼近  

H^1—Galerkin Nonconforming Mixed Finite Element Approximation of Telegraph Equations

作　　者：李永献[1] 石东伟[2] 

机构地区：[1]河南城建学院数理学院,河南平顶山467036 [2]河南科技学院数学科学学院,河南新乡453003

出　　处：《数学的实践与认识》2015年第6期286-293,共8页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11271340);河南城建学院科研基金(2015JZD007)

摘　　要：在几乎均匀矩形剖分下取双线性Q_(11)元和类Wilson元为逼近空间,研究了一类电报方程的H^1-Galerkin非协调混合有限元方法.利用单元的特殊性质,积分恒等式和平均值技巧,在不需要验证LBB相容性条件及抛弃传统的Ritz投影的情形下,得到了半离散和全离散格式下原始变量及流量分别在H^1模和H(div,Ω)模意义下的超逼近性质.进一步地,借助插值后处理技术,导出了相应的整体超收敛结果.By selecting the bilinear Qn element and quasi-Wilson element as approximating spaces,an H^1-Galerkin nonconforming mixed finite element method is studied for a kind of telegraph equations on almost uniform rectangle subdivision.With the help of the special properties of the above elements,integral identity and mean-value technique,the superclose properties for the primitive solution in broken H^1-norm and the flux in H（div,Ω） norm for semi-discrete and fully-discrete schemes are obtained respectively,without requiring the LBB consistency condition and traditional Ritz projection operator.Furthermore,through employing interpolated postprocessing approach,the corresponding superconvergence results are deduced.

关 键 词：电报方程 H1-Galerkin混合有限元 类WILSON元 超逼近 半离散和全离散格式 

分 类 号：O241.82[理学—计算数学]