A study of discontinuous Galerkin methods for thin bending problems

Abstract

Various continuous/discontinuous Galerkin formulations are examined for the analysis of thin plates. These methods rely on weak imposition of continuity of the normal slope across element boundaries. We draw here upon developments in discontinuous Galerkin methods for second-order elliptic equations, for which several unconditionally stable methods are known, and present continuous/discontinuous Galerkin formulations for bending problems inspired by these methods. For each approach, benchmark simulations have been performed and compared. Also, conclusions are drawn on to the computational ef ciency of the different methods.