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Method of asymptotic partial decomposition of domain. (English) Zbl 0940.35026

Summary: A new method of partial decomposition of a domain is proposed for partial differential equations, depending on a small parameter. It is based on the information about the structure of the asymptotic solution in different parts of the domain. The principal idea of the method is to extract the subdomain of singular behavior of the solution and to simplify the problem in the subdomain of regular behavior of the solution. The special interface conditions are imposed on the common boundary of these partially decomposed subdomains. If, for example, the domain depends on the small parameter and some parts of the domain change their dimension after the passage to the limit, then the proposed method reduces the initial problem to the system of equations posed in the domains of different dimensions with the special interface conditions.

MSC:

35B25 Singular perturbations in context of PDEs
65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
35A35 Theoretical approximation in context of PDEs
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