An arbitrary-order BGG-based discrete scheme for the Reissner--Mindlin plate problem on polygonal meshes

RESUMO

We design and analyse an arbitrary-order numerical scheme for the Reissner--Mindlin plate problem on general polygonal meshes. The scheme is derived from the Hodge--Laplacian associated with a discrete Bernstein--Gelfand--Gelfand (BGG) twisted complex and exploits a discrete $H_2$-based construction for the transverse displacement. We establish a discrete Korn inequality for the underlying Discrete de Rham method (DDR) spaces and prove the convergence of the method. At the lowest order, the analysis yields an error estimate that is uniform with respect to the plate thickness, showing that the scheme is locking-free. Numerical experiments on several families of polygonal meshes support the theoretical results and illustrate the benefits of the enhanced continuity of the transverse displacement discretisation.