A dual finite element complex on the barycentric refinement |
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Authors: | Annalisa Buffa Snorre H Christiansen |
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Institution: | Istituto di Matematica Applicata e Tecnologie Informatiche - CNR, Via Ferrata 1, 27100 Pavia, Italy ; CMA c/o Matematisk Institutt, PB 1053 Blindern, Universitetet i Oslo, NO-0316 Oslo, Norway |
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Abstract: | Given a two dimensional oriented surface equipped with a simplicial mesh, the standard lowest order finite element spaces provide a complex centered on Raviart-Thomas divergence conforming vector fields. It can be seen as a realization of the simplicial cochain complex. We construct a new complex of finite element spaces on the barycentric refinement of the mesh which can be seen as a realization of the simplicial chain complex on the original (unrefined) mesh, such that the duality is non-degenerate on for each . In particular is a space of -conforming vector fields which is dual to Raviart-Thomas -conforming elements. When interpreted in terms of differential forms, these two complexes provide a finite-dimensional analogue of Hodge duality. |
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Keywords: | |
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