A dual finite element complex on the barycentric refinement

By Annalisa Buffa, Snorre H. Christiansen. Mathematics of Computation, 2005

343 citations recorded by the source corpus.

Abstract A simplicial mesh on an oriented two-dimensional surface gives rise to a complex X • 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 • , centered around curl conforming vector fields, naturally isomorphic to the simplicial chain complex on the original mesh and such that Y 2 − 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. I 340 (2005).

Subfields: Computational Mechanics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/c35317a3b6bef4bef95eeb95bd1455738bba72ff

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In Computational Mechanics

In Geometry and Topology

Snorre H. Christiansen

Citations in the corpus

Mimetic finite difference method (2014, background): “In this respect, we also mention the work in [138] [139] and the extensions proposed in [59] [60].”
A multiplicative Calderón preconditioner for the electric field integral equation (2008, methodology): “The proposed preconditioner adopts a discretization of the dual of the range of T on the barycentric mesh using the Buffa-Christiansen (BC) divconforming basis functions fBC [5].”