Hilbert伴随算子逆定理在有限元法中的应用  

APPLICATION OF THE THEOREM OF INVERSE HILBERT—ADJOINT OPERATOR IN FINITE ELEMENT METHOD

作　　者：纪振义[1] 

机构地区：[1]安徽建筑工业学院

出　　处：《上海力学》1993年第3期37-47,共11页Chinese Quarterly Mechanics

基　　金：国家自然科学基金

摘　　要：固体力学或其它学科的大量问题均归结为求解偏微分方程组。本文把 Hilbert 伴随算子逆定理用于有限元法,求解非正定和正定偏微分方程组。它可以带有任意变系数及复杂的边界条件。文小给出了收敛性证明。并给出统一的计算公式。利用本文的方法,可以给出一个非协调有限元。单元之间的协调连续条件仅需在节点上满足,因此很容易处理。和一般的有限元法相比,有更高的精度。文末给出算例,表明利用本文方法获得的解可以收敛于精确解,并有较高的收敛精度。Many problems in solid mechanics and other subjects can be reduced to solve a system of partialdifferential equations.In this paper,the inverse Hilbert-adjoint operator is applied to finite elementmethod to solve positive or non-positive system of partial differential equations with arbitrary variablecoefficients and complicated boundary conditions.In this paper,the convergency of the solution isproved and general formulas for the computation using FEM are given.Besides,an incompatible FEMis derived,by which the compatibility condition between elements can be treated easily provided thatthe compatible continuous conditions may be satisfied on nodes.The derived method has high con-vergency as compared with the general FEM.Numerical examples are given at the later part of this paper,all computational results converge tothe exact solution closely and quickly.

关 键 词：伴随算子 逆定理 有限元法 

分 类 号：O242.21[理学—计算数学]