Adaptive Morley element algorithms for the biharmonic eigenvalue problem

Abstract

This paper is devoted to the adaptive Morley element algorithms for a biharmonic eigenvalue problem in R n (n ≥ 2). We combine the Morley element method with the shifted-inverse iteration including Rayleigh quotient iteration and the inverse iteration with fixed shift to propose multigrid discretization schemes in an adaptive fashion. We establish an inequality on Rayleigh quotient and use it to prove the efficiency of the adaptive algorithms. Numerical experiments show that these algorithms are efficient and can get the optimal convergence rate. MSC: 65N25; 65N30; 65N15

The Status Quo and Prospect of Model-free Adaptive Control

“…The model-free adaptive control method is to realize the adaptive control system by calculating the input and output data of the controlled system and generating a reasonable system driving amount, so that the deviation between the actual value and the set value of the system output becomes smaller. The method of control [2] . The controller based on model-free adaptive control has the advantages of good tracking performance and easy implementation.…”