Dear Firedrakers,

I would like to solve equations in a domain made of two subdomains:

- a disk, inside which test functions are continuous (Omega_d)

- a plane around the disk, in which test functions are continuous (Omega_p)

However, I would like the test functions to be discontinuous across the interface Gamma between the disk and the surrounding plane.

This is to solve Laplace equation in each domain, augmented by a dynamic boundary condition on the jump between the two domains, that is

Delta u = 0 in Omega_d

Delta u = 0 in Omega_p

partial_t [u] = ...   on Gamma, where [u]= u(+)-u(-) is the jump

Is there a way to define a functionspace on the full mesh, with continuous basis functions in each subdomain but discontinuous across the interface ? Or is there any better way to solve this kind of system ?

Thank you for your help,

Floriane