A Posteriori Error Estimates for Local $C^0$ Discontinuous Galerkin Methods for Kirchhoff Plate Bending Problems

Abstract

We derive some residual-type a posteriori error estimates for the local $C^0$ discontinuous Galerkin (LCDG) approximations ([31]) of the Kirchhoff bending plate clamped on the boundary. The estimator is both reliable and efficient with respect to the moment-field approximation error in an energy norm. Some numerical experiments are reported to demonstrate theoretical results.