  We study nonlocal Dirichlet energies associated with a class of nonlocal
diffusion models on a bounded domain subject to the conventional local
Dirichlet boundary condition. The Dirichlet boundary condition is imposed
through a specifically designed penalty formulation. We prove that the nonlocal
Dirichlet energies with the penalty terms converge to local Dirichlet energies
with Dirichlet boundary conditions in the sense of $\varGamma$-convergence.
