A Dirichlet boundary value problem for a delay parabolic differential equation is studied on a
rectangular domain in the xt plane. The second-order space derivative is multiplied by a
small singular perturbation parameter, which gives rise to parabolic boundary layers on the
two lateral sides of the rectangle. A numerical method comprising a standard finite difference
operator (centred in space, implicit in time) on a rectangular piecewise uniform fitted mesh of
Nx× Nt elements condensing in the boundary layers is proved to be robust with respect to