Title:  LOCAL APPROXIMATIONS OF THE STEKLOV POINCARE OPERATOR
FOR A CLASS OF ELLIPTIC OPERATORS,
AND DOMAIN DECOMPOSITION METHODS.

Authors: Y. Achdou* and F.Nataf**
*      e-mail  achdou@cmapx.polytechnique.fr
**   e-mail  nataf@cmapx.polytechnique.fr

Abstract:
Many implicit Navier Stokes solvers involve the discretization of 
an elliptic partial differential equation of the type  $-\Delta u+ \eta u =f$, where
$\eta$ is a large positive parameter. The discretization studied here is
the mortar finite element method, a domain decomposition method allowing non matching meshes at
subdomains interfaces. Two kinds of improvements are proposed here in order to reduce the condition
number of the corresponding linear systems :
the first one lies on building preconditioners by approximating Steklov-Poincar\'e
operators on subdomains boundaries by second order partial differential operators; the second
one consists in making a non standard choice of jump operators at subdomains interfaces.
Both ideas are tested numerically.

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in the directory pub/RI/1994 under the name

                 achdou_nataf_303.sept.ps.gz