In this work, we propose a novel formulation for the solution of partial differential equations
using finite element methods on unfitted meshes. The proposed formulation relies on the
discrete extension operator proposed in the aggregated finite element method. This
formulation is robust with respect to the location of the boundary/interface within the cell.
One can prove enhanced stability results, not only on the physical domain, but on the whole
active mesh. However, the stability constants grow exponentially with the polynomial order …