A dual finite element complex on the barycentric refinement

A simplicial mesh on an oriented two-dimensional surface gives rise to a complex X-center dot of finite element spaces centered on divergence conforming Raviart-Thomas vector fields and naturally isomorphic to the simplicial cochain complex. On the barycentric refinement of such a mesh, we construct finite element spaces forming a complex Y-center dot, centered around curl conforming vector fields, naturally isomorphic to the simplicial chain complex on the original mesh and such that Y2-i is in L-2 duality with X-i. In terms of differential forms this provides a finite element analogue of Hodge duality. To cite this article: A. Buffa, S.H. Christiansen, C. R. Acad. Sci. Paris, Ser. 1340 (2005). (c) 2005 Academie des sciences. Published by Elsevier SAS. All rights reserved.