Summary: Contemporary Mathematics
Nonmatching grids for fluids
Yves Achdou, Gassan Abdoulaev, JeanClaude Hontand, Yuri A.
Kuznetsov, Olivier Pironneau, and Christophe Prud'homme
We review some topics about the use of nonmatching grids for fluids. In a
first part, we discuss the mortar method for a convection diffusion equation. In a
second part, we present a three dimensional NavierStokes code, based on mortar
elements, whose main ingredients are the method of characteristics for convection,
and a fast solver for elliptic equations for incompressibility. Finally, preliminary
numerical results are given.
Since the late nineteen eighties, interest has developed in nonoverlapping do
main decomposition methods coupling different variational approximations in dif
ferent subdomains. The mortar element methods, see , , have been de
signed for this purpose and they allow us to combine different discretizations in
an optimal way. Optimality means that the error is bounded by the sum of the
subregionbysubregion approximation errors without any constraints on the choice
of the different discretizations. One can, for example couple spectral methods with
finite elements, or different finite element methods with different meshes.
The advantages of the mortar method are: