A Multiscale Finite Element Method Applied to a Neuroscience Problem

Abstract

Several interesting problems in neuroscience are of multiscale type, i.e. possesses different temporal and spatial scales that cannot be disregarded. Such characteristics impose severe burden to numerical simulations since the need to resolve small scale features push the computational costs to unreasonable levels. Classical numerical methods that do not resolve the small scales suffer from spurious oscillations and lack of precision. This paper presents a finite element method of multiscale type that is easy to parallelize and that ameliorates these maladies. We show the validity of our scheme under different physiological regimes.