Communications on Applied Mathematics and Computation ›› 2023, Vol. 5 ›› Issue (4): 1697-1712.doi: 10.1007/s42967-023-00266-w

• ORIGINAL PAPERS • Previous Articles    

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

Shangyou Zhang   

  1. Department of Mathematical Sciences, University of Delaware, Newark, DE 19716, USA
  • Received:2022-10-23 Revised:2023-02-18 Published:2023-12-16
  • Contact: Shangyou Zhang,E-mail:szhang@udel.edu E-mail:szhang@udel.edu

Abstract: The family of Falk-Neilan Pk finite elements, combined with the Argyris Pk+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.

Key words: Locking free, Reissner-Mindlin equation, Finite element, Triangular grids

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