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 adjoint, second order elliptic problems and quadrilateral elements in the finite 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 variant of the method on the interface. Numerical experiments confirming these results are reported. As is the case for other additive Schwarz methods, our algorithms are highly parallel and scalable.