A block-circulant preconditioner for domain decomposition algorithm for the solution of the elliptic problems by second order finite elements

Abstract

A preconditioned conjugate gradient domain decomposition method was given Refs 1 and 2 for the solution of a system of linear equations arising in the finite element method applied to the elliptic Dirichlet, Neumann and mixed boundary value problems. We have proved that the construction can be generalized² for higher order finite element method. Here we give a construction and theoretical investigation of preconditioners for second order finite elements. A method and the the results of calculation is given. The presented numerical experiments show that this preconditioner works well.