  We consider a one-dimensional singularly perturbed 4th order problem with the
additional feature of a shift term. An expansion into a smooth term, boundary
layers and an inner layer yields a formal solution decomposition, and together
with a stability result we have estimates for the subsequent numerical
analysis. With classical layer adapted meshes we present a numerical method,
that achieves supercloseness and optimal convergence orders in the associated
energy norm. We also consider coarser meshes in view of the weak layers. Some
numerical examples conclude the paper and support the theory.
