Realistic eigenvalue bounds for the Galerkin mass matrix. (English) Zbl 0648.65076

Wathen, A. J.

IMA J. Numer. Anal. 7, 449-457 (1987).

Lower and upper bounds on the eigenvalues of the Galerkin mass matrix being preconditioned by its diagonal entries are derived. The bounds are established in an element-by-element manner using the matrix representation of the assembly rules. The results support the conjecture that the diagonally preconditioned conjugate gradients are an efficient solver for the Galerkin mass matrix equations.

Reviewer: D.Janovska

MSC:

65N30	Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
74S05	Finite element methods applied to problems in solid mechanics
65F15	Numerical computation of eigenvalues and eigenvectors of matrices
15A42	Inequalities involving eigenvalues and eigenvectors
65F10	Iterative numerical methods for linear systems
35J25	Boundary value problems for second-order elliptic equations

Keywords:

finite elements; Lower and upper bounds; eigenvalues; Galerkin mass matrix; diagonally preconditioned conjugate gradients