Preconditioning of the Stiffness Matrix of Local Refined Triangulation

Abstract

A preconditioning method for the finite element stiffness matrix is given in this paper. The triangulation is refined in a subregion; the preconditioning process is composed of resolution of two regular subproblems; the condition number of the preconditioned matrix is $O(1+log\frac{H}{h})$, where $H$ and $h$ are mesh sizes of the unrefined and local refined triangulation respectively.