  For a sequence of coupled fields $\{(\phi_n,\psi_n)\}$ from a compact Riemann
surface $M$ with smooth boundary to a general compact Riemannian manifold with
uniformly bounded energy and satisfying the Dirac-harmonic system up to some
uniformly controlled error terms, we show that the energy identity holds during
a blow-up process near the boundary. As an application to the heat flow of
Dirac-harmonic maps from surfaces with boundary, when such a flow blows up at
infinite time, we obtain an energy identity.
