A robust nonconforming \(H^2\)-element
Finite element methods for some elliptic fourth-order singular perturbation problems are considered. It is shown that if such problems are discretized by the nonconforming Morley method, in a regime close to second-order elliptic equations, then the error increases. A counterexample is presented to show that the Morley method diverges for the reduced second-order equation.NEWLINENEWLINENEWLINEAn alternative to the Morley method is proposed to use a nonconforming \(H^2\)-element which is \(H^1\)-conforming. It is shown that the new finite element method converges in the energy norm uniformly in the perturbation parameter.
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