On the Relation Between the Convergence Factors of Additive and Multiplicative Schwarz Method

1 Additive and Multiplicative Schwarz Method Let ΩR~n be a polygonal region, be the variational form of an elliptic boundary value problem defined on Ω. a(·,·) is symmetric positive definite and it introduces an inner product in H~1~0(Ω) which is equivalent to the original one. In the following, we treat H~1(Ω) as a Hilbert space with inner product a(·,·).