An Isoparametric Finite Element Method for Reissner-Mindlin Plate Problem on Curved Domain

Abstract

In this paper, we present an application of the isoparametric finite element for the Reissner-Mindlin plate problem on bounded domain with curved boundary. The discrete scheme is established by isoparametric quadratic triangular finite element combined with a numerical quadrature. Under the certain numerical quadrature, we prove the existence and uniqueness of the numerical solutions and the error estimates of optimal order in $H^1$-norm are given in details with the help of rigorous analysis. Finally, a numerical example is provided to verify the theoretical results.