A Robust Nonconforming H 2 { Elementtrygve

Finite element methods for some elliptic fourth order singular perturbation problems are discussed. We show that if such problems are discretized by the nonconforming Morley method, in a regime close to second order elliptic equations, then the error deteriorates. In fact, a counter example is given to show that the Morley method diverges for the reduced second order equation. As an alternative to the Morley element we propose to use a noncon-forming H 2 {element which is H 1 {conforming. We show that the new element converges in the energy norm uniformly in the perturbation parameter under suitable regularity assumptions on the solution.