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2006•Numerical Linear Algebra with ApplicationsRequires access

Improvements for some condition number estimates for preconditioned system in p ‐FEM

Sven Beuchler, Dietrich Braess

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Abstract

Abstract In this paper, we consider domain decomposition preconditioners for a system of linear algebraic equations arising from the p ‐version of the FEM. We analyse several multi‐level preconditioners for the Dirichlet problems in the sub‐domains in two and three dimensions. It is proved that the condition number of the preconditioned system is bounded by a constant independent of the polynomial degree. Relations between the p ‐version of the FEM and the h ‐version are helpful in the interpretations of the results. Copyright © 2006 John Wiley & Sons, Ltd.

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What this paper is about

Abstract In this paper, we consider domain decomposition preconditioners for a system of linear algebraic equations arising from the p ‐version of the FEM. We analyse several multi‐level preconditioners for the Dirichlet problems in the sub‐domains in two and three dimensions. It is proved that the condition number of the preconditioned system is bounded by a constant independent of the polynomial degree. Relations between the p ‐version of the FEM and the h ‐version are helpful in the interpretations of the results. Copyright © 2006 John Wiley & Sons, Ltd.

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Available abstract

Abstract In this paper, we consider domain decomposition preconditioners for a system of linear algebraic equations arising from the p ‐version of the FEM. We analyse several multi‐level preconditioners for the Dirichlet problems in the sub‐domains in two and three dimensions. It is proved that the condition number of the preconditioned system is bounded by a constant independent of the polynomial degree. Relations between the p ‐version of the FEM and the h ‐version are helpful in the interpretations of the results. Copyright © 2006 John Wiley & Sons, Ltd.

Key concepts: Mathematics, Finite element method, Bounded function, Domain decomposition methods, Condition number, Constant (computer programming), Polynomial, Algebraic equation

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