Lf. Pavarino et Ob. Widlund, A POLYLOGARITHMIC BOUND FOR AN ITERATIVE SUBSTRUCTURING METHOD FOR SPECTRAL ELEMENTS IN 3 DIMENSIONS, SIAM journal on numerical analysis, 33(4), 1996, pp. 1303-1335
Iterative substructuring methods form an important family of domain de
composition algorithms for elliptic finite element problems. A p-versi
on 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 eleme
nt method. An iterative method is designed for which the condition num
ber of the relevant operator grows only in proportion to (1 + log p)(2
). This bound is independent of jumps in the coefficient of the ellipt
ic problem across the interfaces between the subregions. Numerical res
ults are also reported which support the theory.