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Numerical approximation of 2D elliptic transmission problem in disjoint domains
Last modified: 2014-01-24
Abstract
An elliptic transmission problem in disjoint domains is investigated. The existence and uniqueness of its weak solution is proved. A finite difference scheme approximating this problem is proposed and analyzed. An estimate of the convergence rate, compatible with the smoothness of the input data (up to a logarithmic factor of the mesh size) is obtained.
Keywords
Transmission problem, disjoint domains, Sobolev spaces, finite difference scheme, convergence rate