I have several questions about the Discrete Exterior Calculus (DEC) in the numerical method for solving partial differential equation in physics:

(Discrete Exterious Calculus is the newly developed subject mainly used in numerical computing, one reference is, for example, Hirani's PhD thesis: Discrete Exterior Calculus)

Has any kind of convergence property been proved?I mean, under what conditions, the numerical solution of DEC scheme will converge to the the actual solution of PDE. I checked many literature and didn't see any material concerning the convergence property, because I am doing engineer problem in computer and if we can't gurantee it will converge then the precision will be a problem.

What is the current status of using DEC to numerically solve equations/simulation in fluid mechnanics, elasticity and electromagnetism, respectively? Should anyone give me some relevant papers, I have found some but just don't know if I missed anything.

Thanks for any help!