  In many situations with finite element discretizations it is desirable or
necessary to impose boundary or interface conditions not as essential
conditions -- i.e. through the finite element space -- but through the
variational formulation. One popular way to do this is Nitsche's method. In
Nitsche's method a stabilization parameter $\lambda$ has to be chosen
"sufficiently large" to provide a stable formulation. Sometimes discretizations
based on a Nitsche formulation are criticized because of the need to manually
choose this parameter. While in the discontinuous Galerkin community variants
of the Nitsche method -- known as "interior penalty" method in the DG context
-- are known which do not require such a manually chosen stabilization
parameter, this has not been considered for Nitsche formulations in other
contexts. We introduce and analyse such a parameter-free variant for two
applications of Nitsche's method. First, the classical Nitsche formulation for
the imposition of boundary conditions with fitted meshes and secondly, an
unfitted finite element discretizations for the imposition of interface
conditions is considered. The introduced variants of corresponding Nitsche
formulations do not change the sparsity pattern and can easily be implemented
into existing finite element codes. The benefit of the new formulations is the
removal of the Nitsche stabilization parameter $\lambda$ while keeping the
stability properties of the original formulations for a "sufficiently large"
stabilization parameter $\lambda$.
