相关论文: Robust approximation of generalized Biot-Brinkman …
Slightly compressible Brinkman-Forchheimer equations in a bounded 3D domain with Dirichlet boundary conditions are considered. These equations model fluids motion in porous media. The dissipativity of these equations in higher order energy…
We study a finite element computational model for solving the coupled problem arising in the interaction between a free fluid and a fluid in a poroelastic medium. The free fluid is governed by the Stokes equations, while the flow in the…
We propose and analyze an augmented mixed finite element method for the pseudostress-velocity formulation of the stationary convective Brinkman-Forchheimer problem in $\mathrm{R}^d$, $d\in \{2,3\}$. Since the convective and Forchheimer…
In this paper we present a mathematical and numerical analysis of an eigenvalue problem associated to the elasticity-Stokes equations stated in two and three dimensions. Both problems are related through the Herrmann pressure. Employing the…
Recently, a widely applicable system of hyperbolic partial differential equations has been derived that enables the deterministic computation of a full heterogeneous stress field from a measured deformation field, for example, from a strain…
We consider the finite element discretization and the iterative solution of singularly perturbed elliptic reaction-diffusion equations in three-dimensional computational domains. These equations arise from the optimality conditions for…
The work investigates a model that combines a convection-diffusion-reaction equation for solute concentration with an unsteady Darcy-Brinkman equation for the flow field, including the Kortweg stress. Additionally, the flow field…
In this work, we illustrate the underlying mathematical structure of mixed-dimensional models arising from the composition of graphs and continuous domains. Such models are becoming popular in applications, in particular, to model the human…
The flow of incompressible fluids through porous media plays a crucial role in many technological applications such as enhanced oil recovery and geological carbon-dioxide sequestration. The flow within numerous natural and synthetic porous…
We present an algorithm for the numerical solution of the equations governing combustion in porous inert media. The discretization of the flow problem is performed by the mixed finite element method, the transport problems are discretized…
We compare three random field discretization strategies for probabilistic identification of spatially varying material parameters in high-resolution finite element models. These strategies are (i) the Karhunen-Lo\`eve expansion, (ii) a…
We address the discretization of two-phase Darcy flows in a fractured and deformable porous medium, including frictional contact between the matrix-fracture interfaces. Fractures are described as a network of planar surfaces leading to the…
Computational formulations for large strain, polyconvex, nearly incompressible elasticity have been extensively studied, but research on enhancing solution schemes that offer better tradeoffs between accuracy, robustness, and computational…
Detailed understanding of the coupling between fluid flow and solid deformation in porous media is crucial for the development biomedical devices and novel energy technologies relating to a wide range of geological and biological processes.…
We propose finite element methods for compressible barotropic Stokes systems. We state convergence results for these methods and outline their proofs. The principal tools of the proofs are higher integrability estimates for the discrete…
Wave propagation problems have many applications in physics and engineering, and the stochastic effects are important in accurately modeling them due to the uncertainty of the media. This paper considers and analyzes a fully discrete finite…
In this paper, we consider a stochastic version of the Cahn-Hilliard-Brinkman model in a smooth two- or three-dimensional domain with dynamical boundary conditions. The system describes creeping two-phase flows and is basically a coupling…
This paper analyses conforming and nonconforming virtual element formulations of arbitrary polynomial degrees on general polygonal meshes for the coupling of solid and fluid phases in deformable porous plates. The governing equations…
We develop and analyse an adaptive fully mixed finite element method for stationary generalized bioconvective flows, where the Navier--Stokes equations with concentration-dependent viscosity are coupled with a conservation law for swimming…
Free boundaries of biofilms advancing on surfaces evolve according to conservation laws coupled with systems of partial differential equations for velocities, pressures and chemicals affecting cell behavior. Thin film approximations lead to…