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We present numerical methods for the solution of the Stokes equations that handle interfacial discontinuities, discontinuous material properties and irregular domains.
In the last 30 years there appeared many new areas for applications of inverse Sturm-Liouville problems, among them boundary value problems with discontinuity conditions inside the interval are connected with discontinuous material properties.
The sharp interface treatment allows discontinuous material property variation at the solid liquid interface.
To deal with the discontinuous material interface in a high-order manner, a specialized quadrature is used in the boundary region.
Such problems are connected with discontinuous material properties, such as heat and mass transfer, varied assortment of physical transfer problems, vibrating string problems when the string loaded additionally with point masses, and diffraction problems[3, 4].
These problems, such as heat, mass transfer (see [1]), and diffraction problems, relate to discontinuous material properties, and their miscellaneous physical applications connected with these problems are found in many literature works, see, e.g., [1 17] and the corresponding references cited therein.
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In all prediction methods, the assumption of rock mass behavior generally represents continuous or discontinuous materials.
Two concepts have been devised with special regard to the mining subsidence process and seem to be adaptable especially to discontinuous materials.
DEM belongs to a family of discrete methods originally proposed by Cundall in 1971 in application to the behaviour of discontinuous materials [ 26].
(3) That is, the reluctivity υ is discontinuous across material borders and nonlinear in ferromagnetic materials.
In such applications, the fundamental radiation variable, the intensity I, is discontinuous across material interfaces.
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