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A mixed finite element method for Darcy flow in fractured porous media with non-matching grids

Carlo D’Angelo, Anna Scotti (2012)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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...

A mixed finite element method for Darcy flow in fractured porous media with non-matching grids∗

Carlo D’Angelo, Anna Scotti (2011)

ESAIM: Mathematical Modelling and Numerical Analysis

Applications of Lie Group Analysis to Mathematical Modelling in Natural Sciences

N. H. Ibragimov, R. N. Ibragimov (2012)

Mathematical Modelling of Natural Phenomena

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...

Gravimetric quasigeoid in Slovakia by the finite element method

Zuzana Fašková, Karol Mikula, Róbert Čunderlík, Juraj Janák, Michal Šprlák (2007)

Kybernetika

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...

Matematické modely a numerické simulace vln cunami

Karel Švadlenka (2012)

Pokroky matematiky, fyziky a astronomie

On the global regularity of $N$ -dimensional generalized Boussinesq system

Kazuo Yamazaki (2015)

Applications of Mathematics

We study the $N$ -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.