High order multi-scale wall-laws, Part I: The periodic case

2 00 7 High Order Multi - Scale Wall - Laws , Part I : the Periodic Case

In this work we present new wall-laws boundary conditions including microscopic oscillations. We consider a newtonian flow in domains with periodic rough boundaries that we simplify considering a Laplace operator with periodic inflow and outflow boundary conditions., we construct high order boundary layer approximations and rigorously justify their rates of convergence with respect to ǫ (the ro...

High order multi-scale wall-laws, Part I : the periodic case

Viscous Conservation Laws, Part I: Scalar Laws

Viscous conservation laws are the basic models for the dissipative phenomena. We aim at a systematic presentation of the basic ideas for the quantitative study of the nonlinear waves for viscous conservation laws. The present paper concentrates on the scalar laws; an upcoming Part II will deal with the systems. The basic ideas for scalar viscous conservation laws originated from two sources: th...

The comparison of two high-order semi-discrete central schemes for solving hyperbolic conservation laws

This work presents two high-order, semi-discrete, central-upwind schemes for computing approximate solutions of 1D systems of conservation laws. We propose a central weighted essentially non-oscillatory (CWENO) reconstruction, also we apply a fourth-order reconstruction proposed by Peer et al., and afterwards, we combine these reconstructions with a semi-discrete central-upwind numerical flux ...

Budgeted Learning, Part I: The Multi-Armed Bandit Case

We introduce and motivate the task of learning under a budget. We focus on a basic problem in this space: selecting the optimal bandit after a period of experimentation in a multi-armed bandit setting, where each experiment is costly, our total costs cannot exceed a fixed pre-specified budget, and there is no reward collection during the learning period. We address the computational complexity ...