Snorre Christiansen: Upwinding in finite element spaces of differential forms

In recent years, a number of finite element spaces compatible with the differential operators grad, curl and div, have been given a unified presentation in the language of differential forms, enabling a likewise unified analysis of discretizations of partial differential equations related to the Hodge Laplacian. I will present a general framework for the construction of finite element spaces of differential forms, allowing for polyhedral meshes and non-polynomial basis functions. We apply it to get a variant of finite element exterior calculus, incorporating a form of upwinding adapted to convection dominated flows.

Published Nov. 29, 2011 9:21 AM - Last modified Apr. 10, 2012 3:08 PM