  For the pure biharmonic equation and a biharmonic singular perturbation
problem, a residual-based error estimator is introduced which applies to many
existing nonconforming finite elements. The error estimator involves the local
best-approximation error of the finite element function by piecewise polynomial
functions of the degree determining the expected approximation order, which
need not coincide with the maximal polynomial degree of the element, for
example if bubble functions are used. The error estimator is shown to be
reliable and locally efficient up to this polynomial best-approximation error
and oscillations of the right-hand side.
