Quasi-optimal convergence rate for an adaptive hybridizable C0 discontinuous Galerkin method for Kirchhoff plates

TL;DR

This paper introduces an adaptive hybridizable C0 discontinuous Galerkin method for Kirchhoff plates, providing a reliable error estimator and analyzing convergence and complexity for improved computational efficiency.

Contribution

It develops a novel adaptive HCDG method with a posteriori error estimation and convergence analysis for Kirchhoff plates, advancing numerical methods in structural mechanics.

Findings

Established quasi-orthogonality and discrete reliability.

Proved contraction property between adaptive iterations.

Analyzed complexity of the adaptive HCDG method.

Abstract

In this paper, we present an adaptive hybridizable $C^0$ discontinuous Galerkin (HCDG) method for Kirchhoff plates. A reliable and efficient a posteriori error estimator is produced for this HCDG method. Quasi-orthogonality and discrete reliability are established with the help of a postprocessed bending moment and the discrete Helmholtz decomposition. Based on these, the contraction property between two consecutive loops and complexity of the adaptive HCDG method are studied thoroughly. The key points in our analysis are a postprocessed normal-normal continuous bending moment from the HCDG method solution and a lifting of jump residuals from inter-element boundaries to element interiors.