In addition to the various uses it was introduced for, the theory of -convergence o.ers a rather natural setting for
discussing and developing nonorthodox approximation methods for variational problems. For certain boundary value problems
involving the bi-Laplacian, sequences of discrete functionals are here de1ned and are shown to -converge to
the corresponding functionals of the continuous problems. The minimizers of the discrete functionals provide converging
approximations to the solution of the limit problem in question. Thus, we obtain approximation schemes that are
nonconforming, but direct, and that can be treated by current algorithms for symmetric and positive de1nite functionals.
The class of problems considered in this paper includes the Stokes problem in 5uid dynamics, the loading problem
of 2-D-isotropic elastostatics, and some boundary value problems of the Kirchho.–Love theory of plates. Also discussed
is an extension of the discretization method that seems suitable for treating more general boundary value problems of
elastic plates, but whose convergence is conditional to a conjecture that remains to be proved. A relevant application to
the so-called Babus9ka paradox is presented.
