Domain with a cut and the corresponding space of Lagrange elements

Question

Hi,

I would like to solve the Poisson problem on a 2D ring domain with a cut, e.g. domain = circle(0,0, radius=2) - circle(0,0, radius=1) - line segment((1,0) to (2,0)). How can I define such a domain together with the corresponding space of Lagrange elements? How can I prescribe nonzero-Dirichlet boundary condition on the line segment? Should I somehow use the jump operator?

Any help is appreciated

Answer 1

Use an external mesh generator, e.g. gmsh. You can then 'mark' the facets on the cut to apply boundary conditions. You'll have to take care marking the facets because you won't be able to use just the coordinate to distinguish between sides.