On the Complementarity of Dual Formulations on Dual Meshes

The finite element method (FEM) using Whitney elements and the finite integral technique (FIT) using dual meshes work both with the metric free global variables. Though the mechanisms of two methods are very different, they both exhibit the analogy to the circuit network. Hence, there exists a similarity between the dual FEM formulations and the dual FIT formulations. This paper analyzes the complementarity of the dual formulations of both methods on dual meshes and emphasizes the complementary energy bounds through numerical experiments. The study supports the idea that the energy bounds are due to the geometry discretization on dual meshes.