New Fourth Order Postprocessing Techniques for Plate Bending Eigenvalues by Morley Element

TL;DR

This paper introduces new fourth-order postprocessing techniques for plate bending eigenvalues using the Morley element, including extrapolation and a posterior error estimates, validated through numerical experiments.

Contribution

It develops and analyzes novel extrapolation and error estimation methods for eigenvalues in plate bending problems with Morley elements, achieving higher accuracy.

Findings

Optimal asymptotic expansion of eigenvalues

Effective extrapolation method for improved eigenvalue accuracy

Numerical results confirm theoretical improvements

Abstract

In this paper, we propose and analyze the extrapolation method and asymptotically exact a posterior error estimate for eigenvalues of the Morley element. We establish an asymptotic expansion of eigenvalues, and prove an optimal result for this expansion and the corresponding extrapolation method. We also design an asymptotically exact a posterior error estimate and propose new approximate eigenvalues with higher accuracy by utilizing this a posteriori error estimate. Finally, several numerical experiments are considered to confirm the theoretical results and compare the performance of the proposed methods.