On the design of locking free ghost penalty stabilization and the relation to CutFEM with discrete extension

Abstract In this note, we introduce a novel stabilization mechanism for Cut Finite Element Methods (CutFEM), generalizing previous ghost penalty techniques in two key aspects: (1) the choice of stabilized quantities and (2) the selection of elements involved in stabilization. This approach notably allows for flexible and precise definitions of the stabilized quantities, including various functionals associated with the discrete solution, such as finite element degrees of freedom. We demonstrate that the kernel of our proposed ghost penalty operator defines a finite element space characterized by discrete extensions, closely related to those previously presented in Burman et al. (Numer Math 152(2):331–369, 2022).