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 generalized 2 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.
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