The injection method for imposing Dirichlet boundary conditions is straightforward to use as one simply overwrites the boundary nodes with the exact boundary data. In [1], the stability properties of a numerical scheme approximating the compressible Navier- Stokes equations using a specific finite-difference summation-by-parts (SBP) operator with injected no-slip boundary conditions were studied. It was shown that the resulting scheme is both energy and entropy stable. In this talk, we generalise the results of [1]. That is, we show that injected Dirichlet boundary conditions leads to provably stable schemes in combination with multidimensional SBP operators with diagonal norm and boundary matrices. We demonstrate the efficacy of the schemes for the linear advection equation. Furthermore, we show that the same approach yields entropy estimates for the compressible Navier-Stokes equations augmented with homogeneous no-slip boundary conditions. [1] A. Gjesteland and M. Svärd, Entropy stability for the compressible Navier-Stokes equations with strong imposition of the no-slip boundary condition. Journal of Com- putational Physics, 470, 111572, 2022.