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Artificial boundary conditions for external boundary problem with a cylindrical inhomogeneity. (Russian, English) Zbl 1114.35016

Zh. Vychisl. Mat. Mat. Fiz. 44, No. 12, 2194-2211 (2004); translation in Comput. Math. Math. Phys. 44, No. 12, 2087-2103 (2004).
Local artificial boundary conditions are constructed in exterior Dirichlet and Neumann boundary value problems for a fairly general formally self-adjoint system of second-order differential equations with piecewise constant coefficients. The coefficients have jumps at an infinite cylindrical sur- face with an arbitrary smooth cross section, and the shape of a truncation surface – the boundary of a circular cylinder with a height and diameter of \(2R\) – is adapted to such inhomogeneity. The artificial boundary conditions are constructed without using explicit formulas for the fundamental matrix. Exist- ence and uniqueness theorems are proved for the original and approximating problems, and an asymp- totically sharp error estimate is derived.

MSC:

35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs
35J15 Second-order elliptic equations
35G15 Boundary value problems for linear higher-order PDEs
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