The INI has a new website!

This is a legacy webpage. Please visit the new site to ensure you are seeing up to date information.

Skip to content

HOP

Seminar

Finite difference approximation of homogenization problems for elliptic equations

Zuazua, E (Autonoma)
Thursday 29 March 2007, 09:00-09:45

Seminar Room 1, Newton Institute

Abstract

In this talk, the problem of the approximation by finite differences of solutions to elliptic problems with rapidly oscillating coefficients and periodic boundary conditions will be discussed.

The mesh-size is denoted by $h$ while $\ee$ denotes the period of the rapidly oscillating coefficient. Using Bloch wave decompositions, we analyze the case where the ratio $h/\ee$ is rational. We show that if $h/\ee$ is kept fixed, being a rational number, even when $h,\ee\to 0$, the limit of the numerical solution does not coincide with the homogenized one obtained when passing to the limit as $\ee\to 0$ in the continuous problem. Explicit error estimates are given showing that, as the ratio $h/\ee$ approximates an irrational number, solutions of the finite difference approximation converge to the solutions of the homogenized elliptic equation. We consider both the 1-d and the multi-dimensional case. Our analysis yields a quantitative version of previous results on numerical homogenization by Avellaneda, Hou and Papanicolaou, among others. This is a joint work with Rafael Orive

Presentation

[pdf ]

Audio

MP3MP3

Video

The video for this talk should appear here if JavaScript is enabled.
If it doesn't, something may have gone wrong with our embedded player.
We'll get it fixed as soon as possible.

Back to top ∧