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 Domain decomposition methods for singularly perturbed problems in composite domains. In: Abstracts of the Fourth Siberian Congress on Applied and Industrial Mathematics (INPRIM-2000), Novosibirsk, 2000. Part II, p. 111.

I.V. Tselishcheva, G.I. Shishkin. Domain decomposition methods for singularly perturbed problems in composed domains // Четвертый сибирский конгресс по прикладной и индустриальной математике, посвященный памяти М.А. Лаврентьева (1900-1980), Новосибирск, 2000 / Тезисы докладов. Часть II. С. 111.