I am trying to pick between the two (for now I am not familiar with any), however they both seem to be badass...
About my problem: I need to solve ~100 coupled advection equations in 3D with DG. Flux in advection is linear and constant, however all equations are nonlinearly coupled with source. I know what I need to do with Rimann problem - solve it at the begining exactly (essentially decompose 100x100 flux matrix, which is in itself block diagonal). I need AMR, good parallel scaling, and maybe in the future some non-trivial geometry.
Both packages seem to have what I need, however I never worked with any of them to know for sure.
Deal_ii seem to have better documentation. However, maybe I will be able to find someone around me familiar with MFEM, maybe.
MFEM seem to me more lightweight, hackable and easy to use, but deal_ii looks more mature.
Performance wise they seem to be comparable.
They both are linked to something which may be important, i.e., petsc, hyper...
In the future, I may want to solve this system in time not only explicitly, but also implicitly or with IMEX
Any input or advice is appreciated,
We can't able to offer the solution for your problem as we are dealing with OpenFOAM.
I suggest you to write the query to Prof. Shivasubramanian Gopalakrishnan who is working in DG.