Robust Falk-Neilan Finite Elements for the Reissner-Mindlin Plate

Abstract

The family of Falk-Neilan $P_k$ finite elements, combined with the Argyris $P_{k+1}$ finite elements, solves the Reissner-Mindlin plate equation quasi-optimally and locking-free, on triangular meshes. The method is truly conforming or consistent in the sense that no projection/reduction is introduced. Theoretical proof and numerical confirmation are presented.