Summary: A Numerical quadrature for the
J. -B. Apoung Kamga1
and Olivier Pironneau2
Laboratoire J.L. Lions, Universit´e Paris VI email@example.com
and Institut Universitaire de france Curie Olivier.Pironneau@upmc.fr
Summary. Chimera  happens to be a version of Schwarz' method and of Lions'
space decomposition method (SDM). It was analyzed by Brezzi et al  but an
estimate was missing for numerical quadrature. We give it here with new numerical
Consider a Hilbert space V , a continuous bilinear form a(u, ^u) symmetric with
a coercivity constant > 0 and f regular enough for well posedness of
a(u, ^u) = (f, ^u) ^u V. (1)
We assume that V = V1 + V2, that V1 V2 is of non zero measure (i.e.
overlapping) where each Vi is a closed subspace of V . We will need also two
continuous symmetric bilinear forms bi(u, ^u), i = 1, 2 coercive enough so that