Preconditioning isoparametric finite element methods taking into account numerical integration

摘要

This paper is concerned with the H1-condition numbers and the Bh-singular value distribution of preconditioned operators {Bh−1Ah}0 < h < 1, where Ah and Bh are isoparametric finite element discretizations of second order elliptic operators A and B, by taking into account numerical integration respectively, where A is nonselfad-joint and possibly indefinite, and B is selfadjoint and positive definite. It is proved that the H1-condition numbers of operators {Bh−1Ah}0 < h < 1 are uniformly bounded, and the Bh-singular values cluster in a positive finite interval. Finally, the implementation of Bh−1 is discussed.