My initial plan was to write a new code using only PETSc. However, I don't see 
how to do what I want within the point-wise residual function. Am I missing 
something?

Yes. I would be interested in collaborating on the ceed-fluids. I took a quick 
look at the links you provided and it looks interesting. I'll warn you though. 
I'm a Mechanical Engineer by trade/training. The calculus and programming 
sometimes take me a little while to wrap my head around. Let me know how I can 
help. In the meantime, I'll continue to review the information you sent over.
________________________________
From: Jed Brown <j...@jedbrown.org>
Sent: Tuesday, October 10, 2023 10:18 PM
To: Brandon Denton <blden...@buffalo.edu>; petsc-users@mcs.anl.gov 
<petsc-users@mcs.anl.gov>
Subject: Re: [petsc-users] FEM Implementation of NS with SUPG Stabilization

Do you want to write a new code using only PETSc or would you be up for 
collaborating on ceed-fluids, which is a high-performance compressible SUPG 
solver based on DMPlex with good GPU support? It uses the metric to compute 
covariant length for stabilization. We have YZƁ shock capturing, though it 
hasn't been tested much beyond shock tube experiments. (Most of our work has 
been low Mach.)

https://libceed.org/en/latest/examples/fluids/
https://github.com/CEED/libCEED/blob/main/examples/fluids/qfunctions/stabilization.h#L76


On Tue, Oct 10, 2023, at 7:34 PM, Brandon Denton via petsc-users wrote:
Good Evening,

I am looking to implement a form of Navier-Stokes with SUPG Stabilization and 
shock capturing using PETSc's FEM infrastructure. In this implementation, I 
need access to the cell's shape function gradients and natural coordinate 
gradients for calculations within the point-wise residual calculations. How do 
I get these quantities at the quadrature points? The signatures for fo and f1 
don't seem to contain this information.

Thank you in advance for your time.
Brandon

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