There are very few results on mixed finite element methods on surfaces. A
theory for the study of such methods was given recently by Holst and Stern,
using a variational crimes framework in the context of finite element exterior
calculus. However, we are not aware of any numerical experiments where mixed
finite elements derived from discretizations of exterior calculus are used for
a surface domain. This short note shows results of our preliminary experiments
using mixed methods for Darcy flow (hence scalar Poisson's equation in mixed
form) on surfaces. We demonstrate two numerical methods. One is derived from
the primal-dual Discrete Exterior Calculus and the other from lowest order
finite element exterior calculus. The programming was done in the language
Python, using the PyDEC package which makes the code very short and easy to
read. The qualitative convergence studies seem to be promising.Comment: 14 pages, 11 figure