# Boundary term in Fenics example is identically zero?

Hello,
Consider the boundary term `dot(p_n*n, v)*ds` on line 80 in this Fenics Navier Stokes Example. I wonder whether this term is identically zero, and thus can be omitted from `F1`.

In fact, at each time step one solves for `p_` with the boundary condition (BC) that `p_` is zero at the `outflow`:

``````bcp_outflow = DirichletBC(Q, Constant(0), outflow)
bcp = [bcp_outflow]

for n in range(num_steps):

[...]

# Step 2: Pressure correction step
b2 = assemble(L2)
[bc.apply(b2) for bc in bcp]
solve(A2, p_.vector(), b2, 'bicgstab', 'hypre_amg')

[...]
``````

then `p_` is stored into `p_n` with `p_n.assign(p_)`.

At the later steps, `p_n` enters into the term `dot(p_n*n, v)*ds` of `F1`: given that `p_n` vanishes on the outflow, `dot(p_n*n, v)*ds` vanishes also on the `outflow`. Also, given that we impose Dirichlet BCs on the velocity on the `inflow` and on the `walls`, `v` vanishes on the `inflow` and on the `walls`, i.e., everywhere.

Is this right?

As far as I can tell you can remove it.

However, there is some good justification for not applying pressure conditions to splitting schemes, see:
https://computationalphysiology.github.io/oasisx/splitting_schemes.html#essential-boundary-conditions