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Whitney forms of higher degree. (English) Zbl 1195.78063
This paper is concerned with the definition of shape functions for high-order Whitney finite element spaces. The main goal in the present paper is to study higher-order Whitney complexes and to design shape functions for Whitney $p$-elements that use only dofs associated with integration subdomains of dimension $p$. This task is performed with the introduction of so-called small simplices, which are defined by means of a particular homothety. Degrees of Freedom are then the integrals over suitable $p$-dimensional subdomains, linear combinations of small $p$-simplices. It is also provided a basis for these elements on simplicial meshes and is given a geometrical localization of all degrees of freedom.

##### MSC:
 78M10 Finite element methods (optics) 65N30 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (BVP of PDE) 68U20 Simulation
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