An Efficient Adaptive Finite Element Method for Eigenvalue Problems

TL;DR

This paper introduces an efficient adaptive finite element method for eigenvalue problems that combines multilevel correction and inverse power methods, improving computational efficiency and verified through theoretical and numerical analysis.

Contribution

It presents a novel adaptive finite element approach that enhances efficiency for eigenvalue problems by integrating multilevel correction and inverse power techniques.

Findings

Convergence and optimal complexity are theoretically proven.

Numerical experiments demonstrate improved efficiency.

Method reduces computational cost for eigenvalue problems.

Abstract

The aim of this paper is to propose an efficient adaptive finite element method for eigenvalue problems based on the multilevel correction scheme and inverse power method. This method involves solving associated boundary value problems on each adaptive partitions and very low dimensional eigenvalue problems on some special meshes which are controlled by the proposed algorithm. Since we Hence the efficiency of solving eigenvalue problems can be improved to be similar to the adaptive finite element method for the associated boundary value problems. The convergence and optimal complexity is theoretically verified and numerically demonstrated.