A discrete de Rham method for the Reissner–Mindlin plate bending problem on polygonal meshes. (1st November 2022)

• Record Type: Journal Article
• Authors: Di Pietro, Daniele A.; Droniou, Jérôme
• Is Part Of: Computers & mathematics with applications. Volume 125(2022)
• Page Start: 136
• Page End: 149
• Publication Date: 2022-11-01
• Subjects: Reissner–Mindlin plates -- Discrete de Rham complex -- Locking free method -- Compatible discretisations -- Polygonal methods; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2022.08.041
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: In this work we propose a discretisation method for the Reissner–Mindlin plate bending problem in primitive variables that supports general polygonal meshes and arbitrary order. The method is inspired by a two-dimensional discrete de Rham complex for which key commutation properties hold that enable the cancellation of the contribution to the error linked to the enforcement of the Kirchhoff constraint. Denoting by k ≥ 0 the polynomial degree for the discrete spaces and by h the meshsize, we derive for the proposed method an error estimate in h k + 1 for general k, as well as a locking-free error estimate for the lowest-order case k = 0 . The theoretical results are validated on a complete panel of numerical tests.