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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:
78M10Finite element methods (optics)
65N30Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (BVP of PDE)
68U20Simulation