Introduction In this paper we consider cell centered nite di erence approximations for second order convection di usion equations of divergence type Our goal is to construct nite di erence methods of second order of approximation that satisfy the discrete maximum principle The error estimates are in the discrete Sobolev spaces associated with the considered boundary value problem Approximation ...

The paper deals with the analysis of pair di usion models in semiconductor technology. The underlying model contains reaction-drift-di usion equations for the mobile point defects and dopant-defect pairs as well as reaction equations for immobile dopants which are coupled with a nonlinear Poisson equation for the chemical potential of the electrons. For homogeneous structures we present an exis...

Di€usion and convection coecients of the aerated ̄ow in a hydraulic jump are estimated in the framework of an optimal control problem. The speci®c gravity of air±water mixture is governed by a steady state convection di€usion partial di€erential equation. The governing equation includes the di€usion coecient and the convection coecient, which are taken as the control variables to minimize a ...

We present a uni ed anisotropic geometric di usion PDEmodel for smoothing (fairing) out noise both in triangulated 2-manifold surface meshes in IR and functions de ned on these surface meshes, while enhancing curve features on both by careful choice of an anisotropic di usion tensor. We combine the C limit representation of Loop's subdivision for triangular surface meshes and vector functions o...

For a number of di usive processes involving heat and mass transfer, a convenient and easy way to solve for penetration time or depth is to consider an averaged quantity called mean action time. This approach was originally developed by Alex McNabb, in collaboration with other researchers. It is possible to solve for mean action time without actually solving the full di usion problem, which may...

A neural network based optimal control synthesis approach is presented for systems modeled by partial di!erential equations. The problem is formulated via discrete dynamic programming and the necessary conditions of optimality are derived. For synthesis of the controller, we propose two sets of neural networks: the set of action networks captures the mapping between the state and control, while...

A simple and e€ective numerical method is proposed for simulating the temporal di€usive mass transport process through a microstructure with arbitrary complexity described by a phase-®eld approach. The mass di€usion through a given microstructure is modeled by a di€usion equation with a variable di€usion coecient, which is solved by an ecient and accurate semi-implicit spectral method. It is ...

In this paper we propose a new numerical approach to the non stationary optical di usion tomography OT problem The assumption in the method is that the absorption and or di usion coe cients are non stationary in the sense that they may exhibit signi cant changes during the time that is needed to measure data for one traditional image frame In the proposed method OT problem is formulated as a st...

Abstract. In this paper we study the pathwise stochastic Taylor expansion, in the sense of our previous work [3], for a class of Itô-type random fields in which the di↵usion part is allowed to contain both the random field itself and its spatial derivatives. Random fields of such an “self-exciting” type particularly contains the fully nonlinear stochastic PDEs of curvature driven di↵usion, as w...

We synthesize robust nonlinear static output feedback controllers for systems of quasi-linear parabolic partial di!erential equations with time-dependent spatial domains and uncertain variables. The controllers are successfully applied to a typical di!usion}reaction process with moving boundary and uncertainty. ( 2000 Elsevier Science Ltd. All rights reserved.