Surface-bulk problem setup

NGSolve
1

Hi everyone!

I would like to implement a bulk-surface equation. The model problem I am considering to begin with is the one presented in 1.1 in the following paper: Finite element analysis for a coupled bulk–surface partial differential equation | IMA Journal of Numerical Analysis | Oxford Academic. It reads:

-\Delta u + u = f \text{ in } \Omega, \\ (\alpha u - \beta \nu) +\frac{\partial u}{\partial n}=0 \text{ on } \Gamma \\ -\Delta_\Gamma\nu +\nu+\frac{\partial u}{\partial n} = g \text{ on } \Gamma

I tried to navigate the forum and find how to deal with having two global fem spaces, one defined on the bulk and one on the boundary of the same bulk:

I wonder if it is, currently, how I should treat this kind of problems or if you had suggestions on how to proceed on setting up the FEM spaces?

Thanks a lot for the help and all the functionality your software provides :slight_smile:

1 Like
2

Hi,
yes, it is as you suggest. These are the components to setup the variational formulation (2.6) from the Elliot+Ranner paper. Let us know if you have any difficulties with it (and also when it works).
Joachim

3

Ok, I see, I will keep you updated, thanks.
Alessandro