Multi-mesh discretization

Hi guys, I want to know how to solve the below problem?

My question is that if the computation domain is separated into several parts, like 3 parts, I want to use P1 on the 1rt part, P2 on the 2nd part and DG on the 3rd part, and implement two interface conditions(one interface condition for 1rt and 2nd part, the other interface condition for 2nd and 3rd part). How should I do that? Can anybody give some tips or demos?

Note that the two interface meshes are matched, i.e., the whole computing mesh on the whole domain is a conforming mesh.


One way is to couple DG and Mixed finite element using Mortar methods. You can have a look at the research article “COUPLING DISCONTINUOUS GALERKIN AND MIXED FINITE ELEMENT DISCRETIZATIONS USING MORTAR FINITE ELEMENTS” by VIVETTE GIRAULTt, SHUYU SUN*, MARY F. WHEELER§, AND IVAN YOTOV*.

This is for 2 subdomain case but you can easily generalize for 3 subdomain case.

Good luck.
Best regards,