 
Summary: A Numerical quadrature for the
SchwarzChimera Method
J. B. Apoung Kamga1
and Olivier Pironneau2
1
Laboratoire J.L. Lions, Universit´e Paris VI apoung@ann.jussieu.fr
2
and Institut Universitaire de france Curie Olivier.Pironneau@upmc.fr
Summary. Chimera [9] happens to be a version of Schwarz' method and of Lions'
space decomposition method (SDM). It was analyzed by Brezzi et al [1] but an
estimate was missing for numerical quadrature. We give it here with new numerical
tests.
1 Introduction
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
2
