# Fourth-order partial differential equation is solved but not satisfied in the bulk **URL:** \ **Category:** General\ **Created:** [January 22, 2025, 9:39pm UTC](https://fenicsproject.discourse.group/t/fourth-order-partial-differential-equation-is-solved-but-not-satisfied-in-the-bulk/16814 "2025-01-22T21:39:02Z")\ **Posts on this page:** 1\ **Showing post:** 3
**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, 8:54am UTC](https://fenicsproject.discourse.group/t/fourth-order-partial-differential-equation-is-solved-but-not-satisfied-in-the-bulk/16814/3 "2025-01-23T08:54:28Z")
> [@Stein](#): > > In your code you only prescribe Dicherlet BCs on `Q.sub(0)` No, I am also imposing boundary conditions on the normal derivative via Nitsche’s method, see ```auto F_N = alpha / r_mesh * ( \ + (((n_circle( omega ))[i] * omega[i] - omega_r) * ((n_circle( omega ))[k] * g( omega )[k, l] * nu_omega[l])) * sqrt_deth_circle( omega, c_r ) * (1.0 / r) * ds_r \ + (((n_circle( omega ))[i] * omega[i] - omega_R) * ((n_circle( omega ))[k] * g( omega )[k, l] * nu_omega[l])) * sqrt_deth_circle( omega, c_R ) * (1.0 / R) * ds_R \ ) [...] F = (F_z + F_omega + F_mu + F_nu) + F_N ``` where `n_circle()` is the boundary normal and \omega\_i = \nabla\_i z. The boundary conditions are correct, I suspect that there is something else… I observed a similar behavior in a simpler example for the bi-harmonic equation to which you replied, I posted it [here](https://fenicsproject.discourse.group/t/problem-solving-fourth-order-pde/16789/7), maybe it can help understand the problem in this post too ! 🙂 Thank you for your help --- _[View the full topic](https://fenicsproject.discourse.group/t/fourth-order-partial-differential-equation-is-solved-but-not-satisfied-in-the-bulk/16814)._