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We consider an incompressible flow problem in a N-dimensional fractured porous domain (Darcy’s problem). The fracture is represented by a (N − 1)-dimensional interface, exchanging fluid with the surrounding media. In this paper we consider the lowest-order (ℝ T0, ℙ0) Raviart-Thomas mixed finite element method for the approximation of the coupled Darcy’s flows in the porous media and within the fracture, with independent meshes for the respective domains. This is achieved thanks to an enrichment...
We consider an incompressible flow problem in a N-dimensional fractured
porous domain (Darcy’s problem). The fracture is represented by a
(N − 1)-dimensional interface, exchanging fluid with the surrounding
media. In this paper we consider the lowest-order (ℝ T0, ℙ0) Raviart-Thomas mixed finite element
method for the approximation of the coupled Darcy’s flows in the porous media and within
the fracture, with independent meshes for the respective...
Today engineering and science researchers routinely confront problems in mathematical modeling involving solutions techniques for differential equations. Sometimes these solutions can be obtained analytically by numerous traditional ad hoc methods appropriate for integrating particular types of equations. More often, however, the solutions cannot be obtained by these methods, in spite of the fact that, e.g. over 400 types of integrable second-order ordinary differential equations were summarized...
The paper presents the solution to the geodetic boundary value problem by the finite element method in area of Slovak Republic. Generally, we have made two numerical experiments. In the first one, Neumann BC in the form of gravity disturbances generated from EGM-96 is used and the solution is verified by the quasigeoidal heights generated directly from EGM-96. In the second one, Neumann BC is computed from gravity measurements and the solution is compared to the quasigeoidal heights obtained by...
We study the -dimensional Boussinesq system with dissipation and diffusion generalized in terms of fractional Laplacians. In particular, we show that given the critical dissipation, a solution pair remains smooth for all time even with zero diffusivity. In the supercritical case, we obtain component reduction results of regularity criteria and smallness conditions for the global regularity in dimensions two and three.
Initial value problem for three dimensional (3D) elastodynamic system in two dimensional (2D) inhomogeneous quasicrystals is considered. An analytical method is studied for the solution of this problem. The system is written in terms of Fourier images of displacements with respect to lateral variables. The resulting problem is reduced to integral equations of the Volterra type. Finally, using Paley Wiener theorem it is shown that the solution of the initial value problem can be found by the inverse...
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