Linking ghost penalty and aggregated unfitted methods

In this work, we analyse the links between ghost penalty stabilisation and aggregation-based discrete extension operators for numerical approximation of elliptic partial differential equations on unfitted meshes. We explore behavior methods in limit as parameter goes to infinity, which returns a strong version these methods. observe that suffer locking limit. On contrary, aggregated finite element spaces are locking-free because they can be expressed an operator from well-posed ill-posed degrees freedom. Next, propose novel penalise distance solution its extension. These converge infinite include exhaustive set experiments compare weak (ghost penalty) (aggregated elements) schemes terms error quantities, condition numbers sensitivity with respect coefficients different geometries, intersection locations mesh topologies.