A Polylogarithmic Bound for an Iterative Substructuring Method for Spectral Elements in Three Dimensions

Authors:
Luca F. Pavarino;Olof B. Widlund
Affiliations:
-;-
Venue:
SIAM Journal on Numerical Analysis
Year:
1996

Citing 0
Cited 10

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Abstract

Iterative substructuring methods form an important family of domain decomposition algorithms for elliptic finite element problems. A $p$-version finite element method based on continuous, piecewise $Q_p$ functions is considered for second-order elliptic problems in three dimensions; this special method can also be viewed as a conforming spectral element method. An iterative method is designed for which the condition number of the relevant operator grows only in proportion to $(1+\log p)^2 .$ This bound is independent of jumps in the coefficient of the elliptic problem across the interfaces between the subregions. Numerical results are also reported which support the theory.