A DPG method for Reissner–Mindlin plates
Thomas Führer, Norbert Heuer, and Antti H. Niemi
SIAM J. Numer. Anal. 61 (2), 995–1017, 2023.
We present a discontinuous Petrov–Galerkin (DPG) method with optimal
test functions for the Reissner–Mindlin plate bending model.
Our method is based on a variational formulation that utilizes a Helmholtz
decomposition of the shear force. It produces approximations of the primitive
variables and the bending moments. For any canonical selection of boundary
conditions the method converges quasi-optimally. In the case of hard-clamped
convex plates, we prove that the lowest-order scheme is locking free.
Several numerical experiments confirm our results.