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Modeling the chemical, electric, and thermal transport as well as phase transitions and the accompanying mesoscale microstructure evolution within a material in an electronic device setting involves the solution of partial differential…
This paper studies field concentration between two nearly touching conductors separated by imperfect low-conductivity interfaces, modeled by Robin boundary conditions. It is known that for any sufficiently small interfacial bonding…
In this paper a generalized fundamental solution using the boundary element method to solve the Helmholtz equation is proposed. It is observed that the commonly used fundamental solution is only valid for good conductors since the…
We study discrete linear divergence-form operators with random coefficients, also known as the random conductance model. We assume that the conductances are bounded, independent and stationary; the law of a conductance may depend on the…
An initial-boundary value problem for the time-fractional diffusion equation is discretized in space using continuous piecewise-linear finite elements on a polygonal domain with a re-entrant corner. Known error bounds for the case of a…
We consider a boundary-value problem describing the steady motion of a two-component mixture of viscous compressible heat-conducting fluids in a bounded domain. We make no simplifying assumptions except for postulating the coincidence of…
We provide a stochastic fractional diffusion equation description of energy transport through a finite one-dimensional chain of harmonic oscillators with stochastic momentum exchange and connected to Langevian type heat baths at the…
We consider the initial/boundary value problem for a diffusion equation involving multiple time-fractional derivatives on a bounded convex polyhedral domain. We analyze a space semidiscrete scheme based on the standard Galerkin finite…
The Cahn--Hilliard equation is a widely used model that describes amongst others phase separation processes of binary mixtures or two-phase flows. In the recent years, different types of boundary conditions for the Cahn--Hilliard equation…
We study the transition to turbulence from the perspective of the velocity gradient tensor dynamics. Our work is motivated by the observation of nonlinear structures emerging during transition, as revealed by vortex identifiers such as the…
We utilize a geometric argument to determine the effects of boundary scattering on the carrier mean-free path in samples of various cross sections. Analytic expressions for samples with rectangular and circular cross sections are obtained.…
A simplified transient energy-transport system for semiconductors subject to mixed Dirichlet-Neumann boundary conditions is analyzed. The model is formally derived from the non-isothermal hydrodynamic equations in a particular vanishing…
We establish stable finite element (FE) approximations of convection-diffusion initial boundary value problems using the automatic variationally stable finite element (AVS-FE) method. The transient convection-diffusion problem leads to…
Analysis of an interface stabilised finite element method for the scalar advection-diffusion-reaction equation is presented. The method inherits attractive properties of both continuous and discontinuous Galerkin methods, namely the same…
Numerical methods: mimetic finite differences and finite elements, are analyzed from a numerical point of view. It seeks to conclude on the efficiency, order of convergence and computational cost of these methods. The analysis is done in…
The third-order Jeffery-Hamel ODE governing the flow of an incompressible fluid in a two-dimensional wedge is briefly derived, and a C^1 finite element formulation of the equation is developed. This formulation has several advantages,…
Mathematical model of the turbulent flux in the three-layer boundary system is presented. Turbulence is described as a presence of the nonzero vorticity. Generalized advection-diffusion-reaction equation is derived for arbitrary number…
Modelling the large deformation of hyperelastic solids under plane stress conditions for arbitrary compressible and nearly incompressible material models is challenging. This is in contrast to the case of full incompressibility where the…
An explicit numerical scheme is proposed for solving the initial-boundary value problem for the radiative transport equation in a rectangular domain with completely absorbing boundary condition. An upwind finite difference approximation is…
This paper introduces a family of transportation costs between non-negative measures. This family is used to obtain parabolic and reaction-diffusion equations with drift, subject to Dirichlet boundary condition, as the gradient flow of the…