A Note on Substructuring Preconditioning for Nonconforming Finite Element Approximations of Second Order Elliptic Problems
نویسنده
چکیده
SUMMARY In this paper an algebraic substructuring preconditioner is considered for non-conforming nite element approximations of second order elliptic problems in 3D domains with a piecewise constant diiusion coeecient. Using a substructuring idea and a block Gauss elimination part of the unknowns is eliminated and the Schur complement obtained is preconditioned by a spectrally equivalent very sparse matrix. In the case of quasiuniform tetrahedral mesh an appropriate algebraic multigrid solver can be used to solve the problem with this matrix. Explicit estimates of condition numbers and implementation algorithms are established for the constructed precon-ditioner. It is shown that the condition number of the preconditioned matrix does not depend neither on mesh step size nor on the jump of the coeecient. Finally, numerical experiments are presented to illustrate the theory being developed.
منابع مشابه
Substructuring Preconditioning for Finite Element Approximations of Second Order Elliptic Problems I Nonconforming Linear Elements for the Poisson Equation in a Parallelepiped
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