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We provide both a general framework for discretizing de Rham sequences ofdifferential forms of high regularity, and some examples of finite elementspaces that fit in the framework. The general framework is an extension of thepreviously introduced notion of Finite Element Systems, and the examplesinclude conforming mixed finite elements for Stokes' equation. In dimension 2we detail four low order finite element complexes and one infinite family ofhighorder finite element complexes. In dimension 3 we define one low ordercomplex, which may be branched into Whitney forms at a chosen index. Stokespairs with continuous or discontinuous pressure are provided in arbitrarydimension. The finite element spaces all consist of composite polynomials. Theframework guarantees some nice properties of the spaces, in particular theexistence of commuting interpolators. It also shows that some of the examplesare minimal spaces.

Generalized Finite Element Systems for smooth differential forms and Stokes problem