A posteriori error estimators suitable for moving finite element methods under anisotropic meshes

TL;DR

This paper introduces a new a posteriori error estimator for moving finite element methods on anisotropic meshes, demonstrating simple computation and high efficiency in numerical experiments for second-order elliptic problems.

Contribution

It presents a novel a posteriori error estimator tailored for anisotropic meshes in moving finite element methods, with straightforward computation based on Hessian recovery.

Findings

Efficient error estimation demonstrated in numerical experiments

Estimator is simple to compute once the Hessian matrix is recovered

High efficiency indices achieved in practical tests

Abstract

In this paper, we give a new type of a posteriori error estimators suitable for moving finite element methods under anisotropic meshes for general second-order elliptic problems. The computation of estimators is simple once corresponding Hessian matrix is recovered. Wonderful efficiency indices are shown in numerical experiments.