We develop a discontinuous ®nite element method for advection±di€usion equations arising in contaminant transport problems, based on the Local Discontinuous Galerkin (LDG) method of Cockburn B and Shu CW. (The local discontinuous Garlerkin method for time-dependent convection±di€usion systems. SIAM J Numer Anal 1998;35:2440±63). This method is de®ned locally over each element, thus allowing for...

We present the mathematical analysis for the convergence of an h version Finite Element Method (FEM) with piecewise polynomials of degree p ≥ 1, de ned on an exponentially graded mesh. The analysis is presented for a singularly perturbed reaction-di usion and a convection-di usion equation in one dimension. We prove convergence of optimal order and independent of the singular perturbation param...

The leaching reaction kinetics of weathered crust elution-deposited rare earth with mixed ammonium salts was studied. The in uence of concentration of reagents and particle size of ore on leaching rate was investigated. The results showed that the di usion process and leaching rate could be improved by increasing reagents concentration and decreasing leaching owing rate and particle size. The l...

The aim of this paper is to investigate the mathematical properties of a continuum model for di usion of multiple species incorporating size exclusion e ects. The system for two species leads to nonlinear cross-di usion terms with double degeneracy, which creates signi cant novel challenges in the analysis of the system. We prove global existence of weak solutions and well-posedness of strong s...

We present a new scheme for the discretization of heterogeneous anisotropic di usion problems on general meshes. With light assumptions, we show that the algorithm can be written as a cell-centered scheme with a small stencil and that it is convergent for discontinuous tensors. The key point of the proof consists in showing both the strong and the weak consistency of the method. Besides, we stu...

In this paper we present a two-step boundary detection algorithm. The "rst step is a nonlinear smoothing algorithm which is based on an orientation-sensitive probability measure. By incorporating geometrical constraints through the coupling structure, we obtain a robust nonlinear smoothing algorithm, where many nonlinear algorithms can be derived as special cases. Even when noise is substantial...

In this work, we apply quantum cellular automata (QCA) to study pattern formation and image processing in quantum-di usion Schrodinger systems (QDSS) with generalized complex di usion coe cients. Generalized complex numbers have the real part and imaginary part with the imaginary unit i = −1 (classical case), i = +1 (double numbers) and i = 0 (dual numbers). They form three 2-D complex algebras...

Parallel primitives (skeletons) intend to encourage programmers to build a parallel program from ready-made components for which e cient implementations are known to exist, making the parallelization process easier. However, programmers often su er from the di culty to choose a combination of proper parallel primitives so as to construct efcient parallel programs. To overcome this di culty, we ...

Abstract. We introduce an algorithm based on semidefinite programming that yields increasing (resp., decreasing) sequences of lower (resp., upper) bounds on polynomial stationary averages of di↵usions with polynomial drift vector and di↵usion coe cients. The bounds are obtained by optimizing an objective, determined by the stationary average of interest, over the set of real vectors defined by ...

We analyze the e ective di usivity of a passive scalar in a two dimensional, steady, incompressible random ow that has mean zero and a stationary stream function. We show that in the limit of small di usivity or large Peclet number, with convection dominating, there is substantial enhancement of the e ective di usivity. Our analysis is based on some new variational principles for convection di ...