Doghonay Arjmand: Exponential decay of the resonance error in homogenisation problems: parabolic and elliptic cell-problems

Abstract:

A common drawback of existing multiscale algorithms for numerical homogenisation problems is the presence of the so-called resonance error. This error is typically much larger than the other errors present in the multiscale methods, and significantly deteriorates the overall accuracy. In recent years, several promising approaches have been proposed to reduce this error. However, the problem still remains open as these approaches come together with some computational challenges. In this talk, starting with a review of the existing approaches, I will talk about two new methods based on the solutions of parabolic and elliptic cell-problems, which result in an exponential decay of the resonance error.