基于二次有限元离散的瀑布型多重网格法及其收敛性  

Convergence Analysis of a Cascadic Multigrid Algorithm Combined with Quadratic Finite Element Method

作　　者：沈红燕 李明[1] SHEN Hong-yan;LI Ming(Department of Mathematics,Honghe University,Mengzi Yunnan 661100,China)

机构地区：[1]红河学院数学学院

出　　处：《西南师范大学学报（自然科学版）》2019年第11期24-28,共5页Journal of Southwest China Normal University(Natural Science Edition)

基　　金：国家重点研发计划项目(2017YFB0701700,2017YFB0305601);云南省科技厅项目(2017FH001-012,2017FH001-015);云南省大学生创新创业训练计划项目(DCXM163005);红河学院大学生创新创业训练计划项目(DCXL151006);红河学院中青年学术带头人后备人才项目(2015HB0304)

摘　　要：通过使用二次有限元的节点信息构造二次插值算子为相邻细网格提供迭代初始值,提出了基于二次有限元离散的瀑布型多重网格法,从理论上分析了该算法的收敛性,给出数值算例验证了改进算法的有效性.A new cascadic multigrid(SECMG) algorithm combined with quadratic finite element method has been proposed, in which a quadratic interpolation operator has been constructed by means of the nodes information of quadratic finite element cell, to provide an initial guess of iterative solution on the next fine grid. The convergence of the developed algorithm has been analyzed. Numerical results have been presented to verify the feasibility of this new method.

关 键 词：二次有限元 二次插值 瀑布型多重网格法 收敛性 

分 类 号：O241[理学—计算数学]