A particularly common step in visual reconstruction is to approximate the solution using a finite element discretization. A variation on the finite element scheme is the use of mixed finite elements, particularly for the systematic approximation of more than one quantity, and the incorporation of constraints into the problem formulation. Mixed finite elements can lead to increased accuracy. Standard finite elements (including the mixed elements) are usually derived by considering each quantity as a single scalar function and designates nodal lattices for each scalar function. Such an approach ignores the richer geometric structure and relationships between various quantities. Whitney Forms provide a systematic means of bringing to bear the machinery of differential geometry into the design of mixed finite element schemes.
David Suter, David Suter,
"Mixed finite elements and Whitney forms for visual reconstruction", Proc. SPIE 2031, Geometric Methods in Computer Vision II, (23 June 1993); doi: 10.1117/12.146645; https://doi.org/10.1117/12.146645