带间断系数椭圆问题的P_1非协调四边形元的加性Schwarz方法

AN ADDITIVE SCHWARZ PRECONDITIONER FOR P_1 NONCONFORMING QUADRILATERAL FINITE ELEMENT METHODSFOR ELLIPTIC EQUATIONS WITH JUMP COEFFICIENTS

本文讨论了带间断系数的二阶椭圆问题的P_1非协调四边形元的加性Schwarz方法.通过分析加性Schwarz预处理后系统的特征值分布,我们证明了除少数小特征值外,其余所有特征值都有正的关于间断系数和网格尺寸拟一致的上下界.数值试验验证了我们的结论.

In this paper, we propose a two level additive Schwarz preconditioner for P1 nonconforming quadrilateral finite element approximations of elliptic equations with jump coefficients. By analyzing the eigenvalue distribution of the additive Schwarz preconditioned systems, we prove that except a small number of eigenvalues, all the other eigenvalues are bounded below and above nearly uniformly with respect to the jump coefficients and meshsize. Therefore, we can get that the convergence rate of the preconditioned conjugate gradient methods is quasi uniform with respect to the large jump and meshsize. Finally, some numerical experiments are presented to confirm our theoretical results.