Related papers: Stable approximation of the advection-diffusion eq…
In this paper, we propose a new formulation and a suitable finite element method for the steady coupling of viscous flow in deformable porous media using divergence-conforming filtration fluxes. The proposed method is based on the use of…
We present a novel hyperviscosity formulation for stabilizing RBF-FD discretizations of the advection-diffusion equation. The amount of hyperviscosity is determined quasi-analytically for commonly-used explicit, implicit, and…
The aim of this paper is to develop and analyze numerical schemes for approximately solving the backward problem of subdiffusion equation involving a fractional derivative in time with order $\alpha\in(0,1)$. After using quasi-boundary…
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…
A hydrogeological model for the spread of pollution in an aquifer is considered. The model consists in a convection-diffusion-reaction equation involving the dispersion tensor which depends nonlinearly of the fluid velocity. We introduce an…
We present a parametric finite element approximation of two-phase flow with insoluble surfactant. This free boundary problem is given by the Navier--Stokes equations for the two-phase flow in the bulk, which are coupled to the transport…
Self-similarity of Burgers' equation with some stochastic advection is studied. In self-similar variables a stationary solution is constructed which establishes the existence of a stochastically self-similar solution for the stochastic…
In this work, we consider the numerical recovery of a spatially dependent diffusion coefficient in a subdiffusion model from distributed observations. The subdiffusion model involves a Caputo fractional derivative of order $\alpha\in(0,1)$…
We study the effect of advection and small diffusion on passive tracers. The advecting velocity field is assumed to have mean zero and to possess time-periodic stream lines. Using a canonical transform to action-angle variables followed by…
In this paper we investigate a sub-diffusion equation for simulating the anomalous diffusion phenomenon in real physical environment. Based on an equivalent transformation of the original sub-diffusion equation followed by the use of a…
We propose certain approach of solving two-dimensional non-stationary and stationary advection-diffusion-reaction boundary value problems through their reduction to the set of corresponding one-dimensional problems. This method leverages…
This work is devoted to the numerical approximation of high-dimensional advection-diffusion equations. It is well-known that classical methods, such as the finite volume method, suffer from the curse of dimensionality, and that their time…
This work consists in two parts. The first part is a review of the finite element method (FEM) for one and two-dimensional problems. The second part, concerns the application of the FEM to find numerical solutions of the Stokes equation and…
We consider planar traveling fronts between stable steady states in two-component singularly perturbed reaction-diffusion-advection equations, where a small quantity $\delta^2$ represents the ratio of diffusion coefficients. The fronts…
For the one dimensional Burgers equation with a random and periodic forcing, it is well-known that there exists a family of invariant measures, each corresponding to a different average velocity. In this paper, we consider the coupled…
In this paper we analyze an optimization problem with limited observation governed by a convection--diffusion--reaction equation. Motivated by a Schur complement approach, we arrive at continuous norms that enable analysis of well-posedness…
Space fractional convection diffusion equation describes physical phenomena where particles or energy (or other physical quantities) are transferred inside a physical system due to two processes: convection and superdiffusion. In this…
In this paper we consider an ESFEM method for the advection and diffusion of a scalar quantity on a moving closed curve. The diffusion process is controlled by a forcing term that may include a rough term (specifically a stochastic noise)…
In this paper, we will provide the the finite element method for the electro-osmotic flow in micro-channels, in which a convection-diffusion type equation is given for the charge density $\rho^e$. A time-discrete method based on the…
The Navier-Stokes-Voigt model of viscoelastic incompressible fluid has been recently proposed as a regularization of the three-dimensional Navier-Stokes equations for the purpose of direct numerical simulations. Besides the kinematic…