# Problem solving fourth-order PDE

**URL:** <https://fenicsproject.discourse.group/t/problem-solving-fourth-order-pde/16789>\
**Category:** General\
**Created:** [January 19, 2025, 6:23pm UTC](https://fenicsproject.discourse.group/t/problem-solving-fourth-order-pde/16789 "2025-01-19T18:23:10Z")\
**Posts on this page:** 1\
**Showing post:** 9

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**Author:** ![mekong](https://yyz2.discourse-cdn.com/free1/user_avatar/fenicsproject.discourse.group/mekong/32/7729_2.png) [@mekong](https://fenicsproject.discourse.group/u/mekong)\
**Post date:** [January 23, 2025, 12:50pm UTC](https://fenicsproject.discourse.group/t/problem-solving-fourth-order-pde/16789/9 "2025-01-23T12:50:57Z")

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> [@Stein](#):
>
> You must substitute the known boundary condition for `- n[i] * v.dx( i )` in place of it,

No, because my boundary conditions (BCs) are Dirichlet BCs. They do not constraint n^i \partial\_i v, see

```auto
bc_u = DirichletBC( Q.sub( 0 ), u_profile, boundary )
bc_v = DirichletBC( Q.sub( 1 ), v_profile, boundary )
[...]
bcs = [bc_u, bc_v]
[...]
problem = NonlinearVariationalProblem( F, psi, bcs, J )

```

I agree with you that I could drop the term `- n[i] * (v.dx( i )) * nu_u * ds` because `nu_u` vanishes, but this previous [post](https://fenicsproject.discourse.group/t/boundary-term-in-fenics-example-is-identically-zero/14995/2) of Dokken’s implies that leaving that term sholud be harmless, because it is zero. Can I get some problems if I leave it ?

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