Related papers: Mixed Mimetic Spectral Element method applied to D…
We study a model describing the slow flow of a fluid through a deformable, porous, elastic solid undergoing small deformations. The stress-strain relationship of the solid incorporates nonlinear effects, formulated as a perturbation of the…
Heterogeneous anisotropic diffusion problems arise in the various areas of science and engineering including plasma physics, petroleum engineering, and image processing. Standard numerical methods can produce spurious oscillations when they…
We consider an elliptic partial differential equation in non-divergence form with a random diffusion matrix and random forcing term. To address this, we propose a mixed-type continuous finite element discretization in the physical domain,…
The micro-continuum method is a novel approach to simulate flow and transport in multiscale porous materials. For such materials, the domain can be divided into three sub-domains depending on the local porosity {\epsilon}: fully resolved…
This paper proposes a parallel numerical algorithm to simulate the flow and the transport in a discrete fracture network taking into account the mass exchanges with the surrounding matrix. The discretization of the Darcy fluxes is based on…
We propose and analyze a combined finite volume--nonconforming finite element scheme on general meshes to simulate the two compressible phase flow in porous media. The diffusion term, which can be anisotropic and heterogeneous, is…
This paper presents the unsteady Darcy's equations coupled with two nonlinear reaction-diffusion equations, namely this system describes the mass concentration and heat transfer in porous media. The existence and uniqueness of the solution…
In this paper we study a stationary double-diffusive natural convection problem in porous media given by a Navier-Stokes/Darcy type system, for describing the velocity and the pressure, coupled to a vector advection-diffusion equation…
In this paper, we present a residual-driven multiscale method for simulating Darcy flow in perforated domains, where complex geometries and highly heterogeneous permeability make direct simulations computationally expensive. To address…
We consider the numerical approximation of compressible flow in a pipe network. Appropriate coupling conditions are formulated that allow us to derive a variational characterization of solutions and to prove global balance laws for the…
The goal of this paper is to develop and analyze some fully discrete finite element methods for a displacement-pressure model modeling swelling dynamics of polymer gels under mechanical constraints. In the model, the swelling dynamics is…
We present a novel artificial diffusion method to circumvent the instabilities associated with the standard finite element approximation of convection-diffusion equations. Motivated by the micromorphic approach, we introduce an auxiliary…
Discrete fracture networks is a key ingredient in the simulation of physical processes which involve fluid flow in the underground, when the surrounding rock matrix is considered impervious. In this paper we present two different models to…
We propose a boundary value correction method for the Brezzi-Douglas-Marini mixed finite element discretization of the Darcy flow with non-homogeneous Neumann boundary condition on 2D curved domains. The discretization is defined on a…
We study a nonlocal diffusion equation of porous medium type featuring a generalised fractional pressure with spatial anisotropy. We construct a finite element method for the numerical solution of the equation on a bounded open Lipschitz…
This paper is concerned with fully discrete finite element methods for approximating variational solutions of nonlinear stochastic elastic wave equations with multiplicative noise. A detailed analysis of the properties of the weak solution…
In the present paper, we study the existence, uniqueness and behaviour in time of the solutions to the Darcy-B\'enard problem for an extended-quasi-thermal-incompressible fluid-saturated porous medium uniformly heated from below. Unlike the…
We study the discretisation of a uniaxial (rank-one) reduction of the Oldroyd-B model for dilute polymer solutions, in which the conformation tensor is represented as $\sig = \vec b \otimes \vec b$. Building on structural analogies with…
We present an implementation of a fully variational formulation of an immersed method for fluid-structure interaction problems based on the finite element method. While typical implementation of immersed methods are characterized by the use…
A discretization of a continuum theory with constraints or conserved quantities is called mimetic if it mirrors the conserved laws or constraints of the continuum theory at the discrete level. Such discretizations have been found useful in…