I am not familiar with the mimetic method so I have a number of questions:

1) Are there any theoretical results which prove the convergence of the mimetic method for a specific set of equations?

2) How do stability results compare?

I also have one suggestion: The steemstem community has a low percentage of individuals with a strong mathematical background. So for most of the community it is not possible to fully enjoy your posts.  To increase your audience and to further promote your work, you could consider to write a simple version of your research results. Would you be interested in that?