Accuracy analysis of the Adini element for biharmonic equation
The authors consider a numerical solution of the Dirichlet boundary value problem of the biharmonic equation using nonconforming finite elements of Adini [cf. \textit{P. G. Ciarlet}, The finite element method for elliptic problems (1978; Zbl 0383.65058)]. First, they develop estimates of the interpolation error and the consistency error due to the nonconformity, then they derive error estimates and further an extrapolation formula using a refinement of the mesh. The authors assume a higher regularity of the solution, they do not, however, explain under which conditions this occurs.
scientific article; zbMATH DE number 2119278