相关论文: A robust iterative scheme for the slightly compres…

This paper is focused on the generalized Forchheimer flows of isentropic gas, described by a system of two nonlinear degenerating differential equations of first order. We prove the existence and uniqueness of the Dirichlet problem for…

We present a continuous and a discontinuous linear Finite Element method based on a predictor-corrector scheme for the numerical approximation of the Ericksen-Leslie equations, a model for nematic liquid crystal flow including a non-convex…

Matrix acidization simulation is a challenging task in the study of flows in porous media, due to the changing porosity in the procedure. The improved DBF framework is one model to do this simulation, and its numerical scheme discretises…

We address in this paper a model for the simulation of turbulent deflagrations in industrial applications. The flow is governed by the Euler equations for a variable composition mixture and the combustion modelling is based on a…

In this paper, we consider numerical approximation of an electrically conductive ferrofluid model, which consists of Navier-Stokes equations, magnetization equation, and magnetic induction equation. To solve this highly coupled, nonlinear,…

This paper considers approximate smoothing for discretely observed non-linear stochastic differential equations. The problem is tackled by developing methods for linearising stochastic differential equations with respect to an arbitrary…

In this paper, we introduce second order and fourth order space discretization via finite difference implementation of the finite element method for solving Fokker-Planck equations associated with irreversible processes. The proposed…

In a porous medium featuring heterogeneous permeabilities, a wide range of fluid velocities may be recorded, so that significant inertial and frictional effects may arise in high-speed regions. In such parts, the link between pressure…

We consider the numerical approximation of a general second order semi--linear parabolic partial differential equation. Equations of this type arise in many contexts, such as transport in porous media which is fundamental in many…

We develop robust and scalable fully implicit nonlinear finite element solvers for the simulations of biological transportation networks driven by the gradient flow minimization of a non-convex energy cost functional. Our approach employs a…

We propose a nonconforming finite element method for isentropic viscous gas flow in situations where convective effects may be neglected. We approximate the continuity equation by a piecewise constant discontinuous Galerkin method. The…

We study the long-time behavior of solutions to the compressible Euler equations with frictional damping in the whole space, where we prescribe direction-dependent values for the density at spatial infinity. To this end, we transform the…

For the Maxwell's equations in a Havriliak-Negami (H-N) dispersive medium, the associated energy dissipation law has not been settled at both continuous level and discrete level. In this paper, we rigorously show that the energy of the H-N…

We introduce a Darcy-scale model to describe compressible multi-component flow in a fully saturated porous medium. In order to capture cross-diffusive effects between the different species correctly, we make use of the Maxwell--Stefan…

A new time discretization scheme for the numerical simulation of two-phase flow governed by a thermodynamically consistent diffuse interface model is presented. The scheme is consistent in the sense that it allows for a discrete in time…

This paper is concerned with the time-step condition of commonly-used linearized semi-implicit schemes for nonlinear parabolic PDEs with Galerkin finite element approximations. In particular, we study the time-dependent nonlinear Joule…

Stratified fluids composed of a sequence of alternate layers show interesting macroscopic properties, which may be quite different from those of the individual constituent fluids. On a macroscopic scale, such systems can be considered a…

We present projection-based mixed finite element methods for the solution of the unsteady Brinkman equations for incompressible single-phase flow with fixed in space porous solid inclusions. At each time step the method requires the…

An implicit Euler finite-volume scheme for general cross-diffusion systems with volume-filling constraints is proposed and analyzed. The diffusion matrix may be nonsymmetric and not positive semidefinite, but the diffusion system is assumed…

An all speed scheme for the Isentropic Euler equation is presented in this paper. When the Mach number tends to zero, the compressible Euler equation converges to its incompressible counterpart, in which the density becomes a constant.…