Convergence of stochastic processes with jumps to diffusion processes is investigated in the case when the limit process has discontinuous coefficients. An example is given in which the diffusion approximation of a queueing model yields a diffusion process with discontinuous diffusion and drift coefficients.

It is well known that the strong error approximation, in the space of continuous paths equipped with the supremum norm, between a diffusion process, with smooth coefficients, and its Euler approximation with step $1/n$ is $O(nˆ{-1/2})$ and that the weak error estimation between the marginal laws, at the terminal time $T$, is $O(nˆ{-1})$. In this talk, we study the $p-$Wasserstein distance betwe...

In this article we analyze a fully discrete numerical approximation to a time dependent fractional order diffusion equation which contains a non-local, quadratic non-linearity. The analysis is performed for a general fractional order diffusion operator. The non-linear term studied is a product of the unknown function and a convolution operator of order 0. Convergence of the approximation and a ...

In this work we show some results about the reduced basis approximation of advection dominated parametrized problems, i.e. advection-diffusion problems with high Péclet number. These problems are of great importance in several engineering applications and it is well known that their numerical approximation can be affected by instability phenomena. In this work we compare two possible stabilizat...

This paper deals with the diffusion approximation of a semiconductor BoltzmannPoisson system. The statistics of collisions we are considering here, is the Fermi-Dirac operator with the Pauli exclusion term and without the detailed balance principle. Our study generalizes, the result of Goudon and Mellet [14], to the multi-dimensional case. keywords: Semiconductor, Boltzmann-Poisson, diffusion a...

in the present article, we focus on the numerical approximation of stochastic partial differential equations of itˆo type with space-time white noise process, in particular, parabolic equations. for each case of additive andmultiplicative noise, the numerical solution of stochastic diffusion equations is approximated using two stochastic finite difference schemes and the stability and consisten...

In this paper, we derive a one-dimensional convection-diffusion model for a rarefied gas flow in a two-dimensional curved channel on the basis of the Boltzmann (BGK) model. The flow is driven by the temperature gradient along the channel walls, which is known as the thermal creep phenomenon. This device can be used as a micro-pumping system without any moving part. Our derivation is based on th...

We propose an arbitrary-order accurate Mimetic Finite Difference (MFD) method for the approximation of diffusion problems in mixed form on unstructured polygonal and polyhedral meshes. As usual in the mimetic numerical technology, the method satisfies local consistency and stability conditions, which determines the accuracy and the well-posedness of the resulting approximation. The method also ...

Abstract The radiative transport equation is solved in the three-dimensional slab geometry by means of the method of rotated reference frames. In this spectral method, the solution is expressed in terms of analytical functions such as spherical harmonics and Wigner d-functions. In addition, the eigenvalues and eigenvectors of a tridiagonal matrix and certain coefficients, which are determined f...

We derive a closed master equation for an individual-based population model in continuous space and time. The model and master equation include Brownian motion, reproduction via binary fission, and an interaction-dependent death rate moderated by a competition kernel. Using simulations we compare this individual-based model with the simplest approximation, the spatial logistic equation. In the ...