Dear Sarraf,

What you’re actually doing here is hand-coding the Galerkin projection into DG0. This is a straight up finite element calculation. In both FEniCS and Firedrake the right way to do this is to let the system do it for you:

DG0 = FunctionSpace(mesh, 'DG', 0)  

Error = project(div(solution), DG0)

Regards,

David

From: <firedrake-bounces@imperial.ac.uk> on behalf of Mohammad Sarraf Joshaghani <m.sarraf.j@gmail.com>
Date: Wednesday, 27 May 2020 at 02:09
To: firedrake <firedrake@imperial.ac.uk>
Subject: [firedrake] Calculate element-wise mass balance

Hello,

I am trying to calculate the element-wise mass balance (i.e., \int_{\Omega_element} div(u) d\Omega) over every cell and project the output to DG0 space. Has this been done or is there a way (e.g., with par_loop() ) to implement this in firedrake?

This is how I achieved it in fenics:

-------------------------------------------------------------------

cell_domains = CellFunction('size_t', mesh)
cell_domains.set_all(0)

dx = Measure('dx')[cell_domains]
area = [cell.volume()   for cell in cells(mesh)]

for i in range(mesh.num_cells()):
    Error.vector()[i]  = (1./area[i]) * assemble(div(solution)*dx(i))

-------------------------------------------------------------------

Regards,

Sarraf