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A dual finite element complex on the barycentric refinement. (English) Zbl 1130.65108

Given a 2-dimensional oriented surface equipped with a simplicial mesh, the standard finite elements of lowest order provide a complex

P 1 elements@>curl>>Raviart-ThomasspaceRT 0 @>div>>P 0 elements.

A new complex of finite element spaces on the barycentric refinement of the mesh is constructed that yield a discrete analogue of

H 1 @>grad>>H(curl)@>curl>>L 2 ·

The only difference is that the functions in the middle space are rotated by the operation uu×n. The resulting spaces are L 2 -dual to the given ones and satisfy an inf-sup condition with constants that are bounded from below for all h.

MSC:
65N12Stability and convergence of numerical methods (BVP of PDE)
65N30Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (BVP of PDE)
65N50Mesh generation and refinement (BVP of PDE)