Komla Domelevo

A Discrete Duality Finite Volume Approach to Hodge Decomposition and div-curl Problems on Almost Arbitrary Two-Dimensional Meshes

We define discrete differential operators such as gradient, divergence, and curl, on general two-dimensional nonorthogonal meshes. These discrete operators verify discrete analogues of usual continuous theorems: discrete Green formulae, discrete Hodge decomposition of vector fields, and vector curls have a vanishing divergence and gradients have a vanishing curl. We apply these ideas to discretize div-curl systems. We give error estimates based on the reformulation of these systems into equivalent equations for the potentials. Numerical results illustrate the use of the method on several types of meshes, some of which are degenerating triangular meshes and nonconforming locally refined meshes.

Solution of a Kinetic Stochastic Equation Modeling a Spray in a Turbulent Gas Flow

This paper studies the modeling of the effect of turbulence on spray. The spray satisfies a kinetic equation. The use of the method of characteristics gives under certain assumptions the solution of the problem. When the gas velocity is modeled by using a white-noise, the solution of the problem satisfies a kinetic stochastic equation and may be written in terms of a Wiener chaos expansion.

Sharp Lp estimates for discrete second order Riesz transforms

We show that multipliers of second order Riesz transforms on products of discrete abelian groups enjoy the Lp estimate p⁎−1, where p⁎=max{p,q} and p and q are conjugate exponents. This estimate is sharp if one considers all multipliers of the form ∑iσiRiRi⁎ with |σi|⩽1 and infinite groups. In the real valued case, we obtain better sharp estimates for some specific multipliers, such as ∑iσiRiRi⁎ with 0⩽σi⩽1. These are the first known precise Lp estimates for discrete Calderon–Zygmund operators.

Existence of pulsating waves in a model of flames in sprays

A one-dimensional system describing the propagation of low Mach number flames in sprays is studied. We show that pulsating waves may exist when the droplet distribution in the unburnt region is spatially periodic. The range of possible propagation speeds may be either bounded or unbounded, depending on the threshold temperatures of the burning and vaporization rates.

Various Sharp Estimates for Semi-discrete Riesz Transforms of the Second Order

We give several sharp estimates for a class of combinations of second-order Riesz transforms on Lie groups G= GxxGy that are multiply connected, composed of a discrete Abelian component Gx and a connected component Gy endowed with a biinvariant measure. These estimates include new sharp Lp estimates via Choi type constants, depending upon the multipliers of the operator. They also include weak-type, logarithmic and exponential estimates. We give an optimal Lq-Lp estimate as well.