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Improvements for some condition number estimates for preconditioned system in p ‐FEM
Author(s) -
Beuchler Sven,
Braess Dietrich
Publication year - 2006
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.489
Subject(s) - mathematics , finite element method , bounded function , domain decomposition methods , condition number , constant (computer programming) , polynomial , algebraic equation , algebraic number , domain (mathematical analysis) , linear system , element (criminal law) , dirichlet distribution , mathematical analysis , nonlinear system , boundary value problem , computer science , law , quantum mechanics , programming language , political science , thermodynamics , eigenvalues and eigenvectors , physics
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.