Integrate solution cell-wise and have it mapped to these cells

Question

Hi, I want to test an estimator. Therefore I have my own norm which is supposed to integrate over each cell and assigning this cell the integral value.
$$
\int_T(\textrm{ grad}\phi_h-\varepsilon^{-1}\sigma_h)^2
$$
My final goal is to have a function (piecewise constants) for each mesh cell containing the error present in this cell and plot it so it can be seen where the biggest error is in the domain (so I can know where to make the mesh finer)
I cannot find out how this is done

Answer 1

You can use DG0 Function:

DG = FunctionSpace(mesh, "DG", 0)
v = TestFunction(DG)
f = 1./CellVolume(mesh)*inner(grad(phi)-1./eps*sigma, v)*dx()
err = Function(DG)
assemble(f, tensor=err.vector())

Comments

Thanks,
It has to be this to work:
1./CellVolume(mesh)*inner(dot(grad(phi)-1./eps*sigma,grad(phi)-1./eps*sigma), v)*dx