# Lost with boundary conditions in ME spaces **URL:** \ **Category:** mathematics\ **Tags:** boundary-conditions\ **Created:** [June 26, 2024, 8:03pm UTC](https://fenicsproject.discourse.group/t/lost-with-boundary-conditions-in-me-spaces/15087 "2024-06-26T20:03:36Z")\ **Posts on this page:** 1\ **Showing post:** 4
**Author:** ![raboynics](https://avatars.discourse-cdn.com/v4/letter/r/4bbf92/32.png) [@raboynics](https://fenicsproject.discourse.group/u/raboynics)\ **Post date:** [July 13, 2024, 12:08pm UTC](https://fenicsproject.discourse.group/t/lost-with-boundary-conditions-in-me-spaces/15087/4 "2024-07-13T12:08:04Z")
I’ve given more thoughts about this observation. My current conclusion is that the claim that vanishing Neumann boundary conditions are applied by default if no boundary conditions are explicitly specified, for a given finite element function, is not correct. And the above MWE is indeed a case where this happens. If you go through the hand derivation of the weak form of the PDE \nabla \cdot \vec J (equivalently, if you integrate this equation over the whole volume and then apply Gauss theorem), you’ll find a different expression than the one I posted in my MWE. In fact, in my MWE, it is exactly the same problem except that I enforce a given electrical current. By doing so, \nabla V has to adjust such that the input and output currents match what I prescribe on the boundaries. And \nabla V does not vanish on all boundaries, in particular those where Dirichlet boundary conditions are specified for the other unknown (temperature in this case). This also responds to [Implementing a potential problem with a current condition - #21 by Daniel.Baker](https://fenicsproject.discourse.group/t/implementing-a-potential-problem-with-a-current-condition/14491/21). I do not believe prescribing the current on the 2 boundaries (in and out current) is insufficient to fully specify the voltage (scalar field). I believe it is perfectly fine, keeping in mind that voltage (or electrostatics potential) is defined up to a constant. I would appreciate if @kamensky could comment. --- _[View the full topic](https://fenicsproject.discourse.group/t/lost-with-boundary-conditions-in-me-spaces/15087)._