  We propose a novel hybrid high-order method (HHO) to approximate singularly
perturbed fourth-order PDEs on domains with a possibly curved boundary. The two
key ideas in devising the method are the use of a Nitsche-type boundary penalty
technique to weakly enforce the boundary conditions and a scaling of the
weighting parameter in the stabilization operator that compares the singular
perturbation parameter to the square of the local mesh size. With these ideas
in hand, we derive stability and optimal error estimates over the whole range
of values for the singular perturbation parameter, including the zero value for
which a second-order elliptic problem is recovered. Numerical experiments
illustrate the theoretical analysis.
