Ragnar Winther
University of Oslo
Abstract: Finite element methods for some elliptic fourth order singular perturbation problems are discussed. 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 deteriorates. In fact, for the reduced second order equation, the Morley method diverges. As an alternative to the Morley element a nonconforming H2-element, which is H1-conforming, is constructed. It is shown that the new finite element method converges in the energy norm uniformly in the perturbation parameter.