Ключевое слово: «perforated domain»

This paper examines fluid flow and transport modeling in porous media, focusing on the influence of Robin boundary conditions. A mixed finite element method is employed to approximate the Stokes equation governing fluid motion. Additionally, the transport equation for substance concentration is analyzed, with solutions obtained using the Streamline Upwind/Petrov-Galerkin (SUPG) method for different diffusion coefficients. The sequential solution approach integrates fluid dynamics and transport phenomena to enhance accuracy. Numerical results are presented for a three-dimensional model, highlighting the interplay between flow, transport, and boundary conditions. This study provides insights into the behavior of fluids in porous structures, aiding ap-plications in fields like hydrology, petroleum engineering, and environmental science.

The elasticity problem is widely used in various fields of engineering and construction, as well as in materials science and mechanics. This work examines the application of elasticity problems for analyzing the behavior of materials under various loads and influences, as well as for calculating deformations and stresses in structures and elements[3]. Numerical modeling of elasticity problems is a relevant and important area in engineering practice. This method makes it possible to predict the behavior of materials under different loads and conditions, which is essential for the design and analysis of various structures. Perforated domains play a key role in engineering applications; however, the presence of holes can significantly affect the mechanical behavior of the material[1]. This article focuses on presenting mathematical models and numerical methods for analyzing the behavior of materials with perforations. Such models make it possible to account for the influence of hole geometry, their sizes, and arrangement on the distribution of stresses and deformations. Numerical modeling is carried out using the finite element method, the FEniCS library, the gmsh program, and visualization in Paraview.