### How to compute functional involving test function

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Generally speaking, how does one compute a post-processing functional involving the computed solution and the test function?

Community: FEniCS Project

### 1 Answer

4

Using the same syntax as usual (The following is a MWE, check out the last couple of lines):

```
from fenics import *
mesh = UnitSquareMesh(4,4)
FE = FiniteElement('Lagrange', mesh.ufl_cell(), 1)
V = FunctionSpace(mesh, FE)
u = TrialFunction(V)
v = TestFunction(V)
# Simple Poisson problem
def boundary(x, on_boundary):
return on_boundary
dbc = DirichletBC(V, Constant(0.), boundary)
f = Expression('pow(x[0],2)', element = FE)
a = inner(grad(u), grad(v))*dx
L = f*v*dx
# u will contain the solution
u = Function(V)
solve(a==L, u, bcs=dbc)
# compute bilinear form with computed solution u
form = assemble(inner(grad(u),grad(v))*dx)
print form.get_local()[:]
```

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