Finite element systems of differential forms and applications to upwinding
University of Oslo
The notion of a finite element system is designed to provide an
alternative to Ciarlet's definition of a finite element, adapted to the
needs of exterior calculus. It allows for cellular decompositions of
space (rather than just simplexes or products thereof) and general
functions (rather than just polynomials) yet guarantees compatibility
with the exterior derivative and existence of commuting interpolation
operators. We review basic definitions and properties. As an
application, we show how a form of upwinding, compatible with the
exterior derivative, can be carried out within this framework.
S. H. Christiansen, H. Z. Munthe-Kaas, B. Owren. Topics in structure-preserving discretization. Acta Numer. 20 (2011), 1-119.
S. H. Christiansen. Upwinding in finite element systems of differential forms. Smale lecture, Proceedings of FoCM 2011, to appear.
Thursday, January 24, 2013
11:00AM AP&M 2402
Center for Computational Mathematics9500 Gilman Dr. #0112La Jolla, CA 92093-0112Tel: (858)534-9056