Related papers: A finite element formulation of the outlet gradien…
A high-order finite element method is proposed to solve the nonlinear convection-diffusion equation on a time-varying domain whose boundary is implicitly driven by the solution of the equation. The method is semi-implicit in the sense that…
In this paper we study a system of advection-diffusion equations in a bulk domain coupled to an advection-diffusion equation on an embedded surface. Such systems of coupled partial differential equations arise in, for example, the modeling…
This dissertation resolves a longstanding discussion of a mathematical problem important in contaminant hydrogeology and chemical-reaction engineering, the proper mathematical description for a miscible solute undergoing longitudinal…
In many applications, transport of particles can be described by the diffusion equation, or its convective-diffusion generalizations, in part of three-dimensional space. In particular, in surface deposition or in growth of aggregates or…
We present a finite element approach for diffusion problems with thermal fluctuations based on a fluctuating hydrodynamics model. The governing transport equations are stochastic partial differential equations with a fluctuating forcing…
We propose a model for the coupling of flow and transport equations with porous membrane-type conditions on part of the boundary. The governing equations consist of the incompressible Navier--Stokes equations coupled with an…
We study the finite element formulation of general boundary conditions for incompressible flow problems. Distinguishing between the contributions from the inviscid and viscid parts of the equations, we use Nitsche's method to develop a…
Long simulation times in climate sciences typically require coarse grids due to computational constraints. Nonetheless, unresolved subscale information significantly influences the prognostic variables and can not be neglected for reliable…
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…
The paper develops a hybrid method for solving a system of advection--diffusion equations in a bulk domain coupled to advection--diffusion equations on an embedded surface. A monotone nonlinear finite volume method for equations posed in…
The conditioning of the linear finite volume element discretization for general diffusion equations is studied on arbitrary simplicial meshes. The condition number is defined as the ratio of the maximal singular value of the stiffness…
A solution is developed for a convection-diffusion equation describing chemical transport with sorption, decay, and production. The problem is formulated in a finite domain where the appropriate conservation law yields Robin conditions at…
We formulate a finite-particle method of mass transport that accounts for general mixed boundary conditions. The particle method couples a geometrically-exact treatment of advection; Wasserstein gradient-flow dynamics; and a…
Consider the steady neutron transport equation in 2D convex domains with in-flow boundary condition. In this paper, we establish the diffusive limit while the boundary layers are present. Our contribution relies on a delicate decomposition…
Convection-diffusion equations provide the basis for describing heat and mass transfer phenomena as well as processes of continuum mechanics. To handle flows in porous media, the fundamental issue is to model correctly the convective…
We develop a cut finite element method (CutFEM) for the convection problem in a so called fractured domain which is a union of manifolds of different dimensions such that a $d$ dimensional component always resides on the boundary of a $d+1$…
A variety of boundary value problems in linear transport theory are expressed as a diffusion equation of the two-way, or forward-backward, type. In such problems boundary data are specified only on part of the boundary, which introduces…
As fractional diffusion equations can describe the early breakthrough and the heavy-tail decay features observed in anomalous transport of contaminants in groundwater and porous soil, they have been commonly employed in the related…
We develop a stabilized cut finite element method for the stationary convection diffusion problem on a surface embedded in ${\mathbb{R}}^d$. The cut finite element method is based on using an embedding of the surface into a three…
In the boundary layer of multicomponent fluid mixtures, the species-specific mass flux in the wall-normal direction is determined by the combination of turbulent-diffusiophoretic diffusion due to composition gradients, and diffusion due to…