Related papers: On One Dimensional Advection -- Diffusion Equation…
An air pollution model is generally described by a system of PDEs on unbounded domain. Transformation of the independent variable is used to convert the problem for nonlinear air pollution on finite computational domain. We investigate the…
We consider the propagation of acoustic time-harmonic waves in a homogeneous media containing periodic lattices of spherical or cylindrical inclusions. It is assumed that the wavelength has the order of the periods of the lattice while the…
We introduce in this paper the numerical analysis of high order both in time and space Lagrange-Galerkin methods for the conservative formulation of the advection-diffusion equation. As time discretization scheme we consider the Backward…
This paper introduces a numerical approach to solve singularly perturbed convection diffusion boundary value problems for second-order ordinary differential equations that feature a small positive parameter {\epsilon} multiplying the…
The dynamics of a freely diffusing particle in a two-dimensional channel with cross sectional area $A(x)$, can be effectively described by a one-dimensional diffusion equation under the action of a potential of mean force $U(x)=-k_BT\ln…
This work studies the parameter-dependent diffusion equation in a two-dimensional domain consisting of locally mirror symmetric layers. It is assumed that the diffusion coefficient is a constant in each layer. The goal is to find…
A system of boundary-domain integral equations is derived from the bidimensional Dirichlet problem for the diffusion equation with variable coefficient using the novel parametrix from [22] different from the one in [5,18]. Mapping…
We consider an inverse problem governed by the Westervelt equation with linear diffusivity and quadratic-type nonlinearity. The objective of this problem is to recover all the coefficients of this nonlinear partial differential equation. We…
We study the transport property of diffusion in a finite translationally invariant quantum subsystem described by a tight-binding Hamiltonian with a single energy band and interacting with its environment by a coupling in terms of…
We present an algorithm for the approximation of a finite horizon optimal control problem for advection-diffusion equations. The method is based on the coupling between an adaptive POD representation of the solution and a Dynamic…
The large time $t$ asymptotics for scalar, constant coefficient,linear, third order, dispersive equations are obtained for asymptotically time-periodic Dirichlet boundary data and zero initial data on the half-line modeling a wavemaker…
A simple finite element formulation of the outlet gradient boundary condition is presented in the general context of convective-diffusive transport processes. Basically, the method is based on an upstream evaluation of the dependent…
Problems with localized nonhomogeneous material properties present well-known challenges for numerical simulations. In particular, such problems may feature large differences in length scales, causing difficulties with meshing and…
In this paper, we introduce and analyse a surface finite element discretization of advection-diffusion equations with uncertain coefficients on evolving hypersurfaces. After stating unique solvability of the resulting semi-discrete problem,…
We study a fractional diffusion problem in the divergence form in one space dimension. We define a notion of the viscosity solution. We prove existence of viscosity solutions to the fractional diffusion problem with the Dirichlet boundary…
We develop a cut finite element method (CutFEM) for convection-diffusion problems posed on mixed-dimensional domains, i.e., unions of manifolds of different dimensions arranged in a hierarchical structure where lower-dimensional components…
This paper considers the Dirichlet problem $$ -\mathrm{div}(a\nabla u_a)=f \quad \hbox{on}\,\,\ D, \qquad u_a=0\quad \hbox{on}\,\,\partial D, $$ for a Lipschitz domain $D\subset \mathbb R^d$, where $a$ is a scalar diffusion function. For a…
Porous materials are widely used for applications in gas storage and separation. The diffusive properties of a variety of gases in porous media can be modeled using molecular dynamics simulations that can be computationally demanding…
In theory, diffusion curves promise complex color gradations for infinite-resolution vector graphics. In practice, existing realizations suffer from poor scaling, discretization artifacts, or insufficient support for rich boundary…
Diffusion is the macroscopic manifestation of disordered molecular motion. Mathematically, diffusion equations are partial differential equations describing the fluid-like large-scale dynamics of parcels of molecules. Spatially…