Discretization error for the Discrete Kirchhoff plate finite element approximation

We provide in this work the discretization error estimates that can guide an adaptive mesh refinement for the Discrete Kirchhoff plate finite elements. The proposed developments are built upon the concept of error estimates for classical elasticity and adapted to suit the Kirchhoff plate finite elements. We give a detailed illustration of the proposed procedures for the Discrete Kirchhoff triangular plate element, along with several different possibilities for constructing the enhancement of test space needed for error estimates. The first novelty concerns the consistent displacement field in terms of the third order polynomial for the Discrete Kirchhoff triangle, whereas the second novelty is the use of the Argyris triangle with fifth order polynomials for constructing the enhanced test for error estimates. We compare the latter against several alternatives that can be used for Kirchhoff plates. The results of numerical examples are given to illustrate the effectiveness of proposed discretization error estimates.