Domain decomposition methods for singularly perturbed
problems in composite domains.
**I.V.Tselishcheva, G.I.Shishkin**
`(Ekaterinburg)`.
Boundary value problems for singularly perturbed parabolic equations
in composed domains, i.e., for equations with a small parameter
e multiplying the highest derivatives and
discontinuous coefficients, often appear in the numerical analysis of
nonstationary heat and mass transfer processes in composite materials
if the coefficients of heat and/or mass transfer are small.
For such problems the application of numerical methods based on
a domain decomposition technique is quite reasonable:
the original domain is naturally partitioned into several
non-overlapping subdomains with smooth coefficients.
Because of transition (inner) and boundary layers, standard numerical
methods yield large errors for small e.
Therefore, there is a need for robust numerical methods that yield
error bounds, in the maximum norm, which are independent of
e, i.e., methods convergent e-uniformly.
To solve the above class of problems considered on sufficiently
simple canonical regions, we construct domain decomposition
finite difference schemes that converge e-uniformly.
For this we use classical finite difference approximations
on piecewise uniform meshes condensing (*a priori*)
in the transition and boundary layers.
We study decomposition parameters for which the number of
iterations in the iterative numerical process does not depend
on the perturbation parameter.
This work was supported by the RFBR grant N 98-01-00362,
and partially by the NWO grant.

I.V.Tselishcheva, G.I.Shishkin

I.V. Tselishcheva, G.I. Shishkin.