A POLYLOGARITHMIC BOUND FOR AN ITERATIVE SUBSTRUCTURING METHOD FOR SPECTRAL ELEMENTS IN 3 DIMENSIONS

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.