# PDE coupling on two meshes

**URL:** <https://community.freefem.org/t/pde-coupling-on-two-meshes/2299>\
**Category:** General Discussion\
**Created:** [March 1, 2023, 10:38am UTC](https://community.freefem.org/t/pde-coupling-on-two-meshes/2299 "2023-03-01T10:38:16Z")\
**Posts on this page:** 1\
**Page:** 1

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**Author:** ![fraphel](https://avatars.discourse-cdn.com/v4/letter/f/898d66/32.png) [@fraphel](https://community.freefem.org/u/fraphel)\
**Post date:** [March 1, 2023, 10:38am UTC](https://community.freefem.org/t/pde-coupling-on-two-meshes/2299/1 "2023-03-01T10:38:16Z")

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Hello,

I am studying the coupling of the bidomain equations (on a 2D finite element mesh **ThB** corresponding ) with a Laplace equation (on a 2D finite element mesh **ThL** ). However I am faced with the following boundary conditions :

- Dirichlet BC : on the common edge between **ThB** and **ThL** I have **uB = uL**. Where **uB** is one of the two unkwown the bidomain equation and **uL** the unknown in the Laplace equation. However, the common edge is not conformal. Should I do an interpolation on this border ? I cheated by considering a little overlapping which leads to a much more satisfactory approximation.

- Neumann BC: on the same common edge, I have **\nabla uB \cdot nB = -\nabla uL \cdot nL** where **nL** (resp. **nB** ) is the unit vector normal to **ThL** (resp. **ThB** ). I then considered :

Thanks a lot !