Curvature boundary condition for 2nd order PDE

5 months ago by
Hello everyone,

I am trying to implement a curvature-based boundary condition for a 2nd order PDE problem. Without going deeply into details, consider we have a system like this (not exactly like I actually have):

 \[au+bu'+cu''=0 \ \ on \ \ \Omega,\\-bu-cu'=\kappa \ \ on \ \ \partial \Omega_{\kappa} ,\\ \kappa =u''\]

Essentially, I have a 2D problem instead of 1D. \(\kappa\) here represents the surface curvature, which arises from a surface tension boundary condition.

As you can see, the usual imposition of the boundary condition will lead to the weak form order increase by one (since we substitute 0 and 1st order boundary terms with 2nd order curvature term).

0 = \int (v,au) - (v', bu + c u') + \int_{\partial \Omega} (v, bu + cu') \rightarrow \int (v,au) - (v', bu + c u')  - \int_{\partial \Omega} (v, u'')
My question is: is it possible to do this in FEM context or should I find a way to somehow remove the 2nd order curvature term?

Thank you in advance!
Community: FEniCS Project

1 Answer

5 months ago by
Hi there,

reviewing the answer of this post may give you some more ideas about the curved boundaries, at least something to start looking

good luck!!
Dear Ruben,

thank you for the link, but I'm not quite sure I understand how are curved boundaries related to my question.
written 5 months ago by Corwinpro  
Please login to add an answer/comment or follow this question.

Similar posts:
Search »