Upwinding in finite element systems of differential forms

Abstract

We provide a notion of finite element system, that enables the construction spaces of differential forms, which can be used for the numerical solution of variationally posed partial difeerential equations. Within this framework, we introduce a form of upwinding, with the aim of stabilizing methods for the purposes of computational uid dynamics, in the vanishing viscosity regime.

Published as the Smale Prize Lecture in: Foundations of computational mathematics, Budapest 2011, London Mathematical Society Lecture Note Series, 403, Cambridge University Press, 2013.