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.
出处
《工程数学学报》
CSCD
北大核心
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)
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
H^1-Galerkin mixed finite element
hyperbolic type integro-differential equations
error estimate
superclose and superconvergence