抛物方程一种新混合有限元格式及误差分析  

A New Mixed Finite Element Formulation and Error Estimates for Parabolic Equations

作　　者：李磊[1] 孙萍[1] 罗振东[1] 

机构地区：[1]贵州师范大学数学与计算机科学学院,贵阳550001

出　　处：《数学物理学报（A辑）》2012年第6期1158-1165,共8页Acta Mathematica Scientia

基　　金：国家自然科学基金(11061009);河北省自然科学基金(A2010001663);贵州省科技计划项目(黔科合J字[2011]2367)资助

摘　　要：研究二维抛物方程,提出一些新的、Brezzi-Babuska条件自然满足的混合变分格式、关于时间半离散混合格式和全离散化混合有限元格式,并对这些格式做严格误差分析.这种混合有限元格式不但自由度是最少的而且所得到的误差估计也是最优阶的,是对现有格式的改进和发展.In this paper,two-dimensional parabolic equations are studied with mixed method. A type of new mixed variational formulations,time-semi-discrete mixed equations,and fully discrete mixed finite element formulations are derived,where Brezzi-Babuska＇s condition is automatically satisfied.And some rigorous error analyses are provided.The degrees of freedom are not only minimum for these mixed finite element formulations,but their error estimates also optimal order.Moreover,it is shown that the methods here are the improvements and renovations for existing all methods.

关 键 词：抛物方程 新的混合变分格式 新的混合有限元格式 误差估计 

分 类 号：O241.4[理学—计算数学]