双曲型积分微分方程一个新H^1-Galerkin混合元格式  

A New H^1-Galerkin Mixed Finite Element Method for the Hyperbolic Type Integro-differential Equation

作　　者：石东洋[1] 王海红[2] 

机构地区：[1]郑州大学数学系,郑州450052 [2]河南财经学院计算机与信息工程学院,郑州450002

出　　处：《工程数学学报》2009年第4期648-652,共5页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(10671184)

摘　　要：在半离散格式下,本文针对一类双曲型积分微分方程,研究了一个新的H1-Galerkin混合有限元方法。该方法不需要满足离散的LBB条件,而且网格剖分不需要满足正则性条件。利用单元的特殊性质,在不需要使用Rita-Volterra投影,而是直接使用插值的情况下,得到了与传统混合有限元方法相同的误差估计,并且得到了超逼近性质。最后,通过使用插值后处理技巧,还得到了相应的超收敛结果。A new H^1-Galerkin mixed finite element method for hyperbolic type integro-differential equations is studied. It is not necessary for our method to satisfy the discrete LBB condition, and the regularity condition is not necessary for the meshes subdivision. By using a special property of the elements, the error estimates, which are as good as that of the traditional mixed finite element methods, are obtained by the interpolation function without Ritz-Volterra projection. Furthermore, the superclose property is derived for the method. Finally, the corresponding global superconvergence is got by taking the advantage of the technique of the post-processing operator.

关 键 词：H1-Galerkin混合元 双曲积分微分方程 误差估计 超逼近和超收敛 

分 类 号：O242.21[理学—计算数学]