自适应间断Galerkin有限元的多水平方法  

Local multilevel methods for adaptive discontinuous Galerkin finite element methods

作　　者：卢培培[1] 石钟慈[1] 许学军[1] 

机构地区：[1]中国科学院数学与系统科学研究院,北京100190

出　　处：《中国科学：数学》2012年第5期409-428,共20页Scientia Sinica：Mathematica

基　　金：国家自然科学基金(批准号:11171335);国家重点基础研究专项经费(批准号:2011CB309701)资助项目

摘　　要：本文讨论在自适应网格上间断Galerkin有限元离散系统的局部多水平算法.对于光滑系数和间断系数情形,利用Schwarz理论分析了算法的收敛性.理论和数值试验均说明算法的收敛率与网格层数以及网格尺寸无关.对强间断系数情形算法是拟最优的,即收敛率仅与网格层数有关.In this paper, the local multilevel methods for discontinuous Galerkin finite element on adaptively refined meshes are considered. By the abstract Schwarz theory, we analyze the convergence rate of the proposed algorithms for smooth and highly discontinuous coefficients separately. It is shown that in the case of smooth coefficients, the convergence rate of the local multilevel methods is independent of mesh sizes and mesh levels. If the coefficients have large jumps, the algorithms are sub-optimal, i.e., the convergence rate is only dependent on mesh levels.

关 键 词：间断有限元 局部多水平算法 间断系数 悬点 

分 类 号：O241.82[理学—计算数学]