ADDITIVE SCHWARZ METHODS FOR THE P-VERSION FINITE-ELEMENT METHOD

In this paper, we study some additive Schwarz methods (ASM) for the p- version finite element method. We consider linear, scalar, self adjoin t, second order elliptic problems and quadrilateral elements in the fi nite element discretization. We prove a constant bound, independent of the degree p and the number of subdomains N, for the condition number of the ASM iteration operator. This optimal result is obtained first in dimension two. It is then generalized to dimension n and to a varia nt of the method on the interface. Numerical experiments confirming th ese results are reported. As is the case for other additive Schwarz me thods, our algorithms are highly parallel and scalable.