FEECa

"FEECa (['fi:ka]) is a library implementing the mathematical framework that the theory of finite element exterior calculus (FEEC), developed by Arnold, Falk and Winther, provides for the discretization of partial differential equations (PDEs) that allows for a universal treatment of a large number of physical problems.

FEECa implements the abstract, mathematical concepts of FEEC and provides a full-fledged basis form generated and framework for computations on differential forms. It handles polynomial differential forms in arbitrary dimensions and implements monomial as well as Bernstein bases for polynomials. The package provides functionality to compute bases of the P_r L^k and P-_r L^k spaces of finite element spaces based on the geometric decomposition proposed by Arnold, Falk and Winther.

Douglas N. Arnold, Richard S. Falk, and Ragnar Winther: Finite element exterior calculus, homological techniques, and applications. J. Acta Numerica. 2006

Douglas N. Arnold, Richard S. Falk, and Ragnar Winther: Geometric decompositions and local bases for spaces of finite element differential forms. J. Computer Methods in Applied Mechanics and Engineering. 2009.
The FEECa online documentation is under construction."

https://github.com/Airini/FEECa