Enhanced error estimator based on a nearly equilibrated moving least squares recovery technique for FEM and XFEM

TL;DR

This paper introduces a new MLS-based error estimator for FEM and XFEM that enforces boundary and internal equilibrium conditions, providing highly accurate energy norm error estimates as an alternative to traditional methods.

Contribution

The paper presents an enhanced MLS recovery technique with boundary equilibrium enforcement and nearly exact internal equilibrium satisfaction for improved error estimation in FEM and XFEM.

Findings

High accuracy of the proposed error estimator demonstrated through numerical results.

Effective enforcement of boundary and internal equilibrium conditions.

Potential to replace traditional superconvergent patch recovery methods.

Abstract

In this paper a new technique aimed to obtain accurate estimates of the error in energy norm using a moving least squares (MLS) recovery-based procedure is presented. We explore the capabilities of a recovery technique based on an enhanced MLS fitting, which directly provides continuous interpolated fields, to obtain estimates of the error in energy norm as an alternative to the superconvergent patch recovery (SPR). Boundary equilibrium is enforced using a nearest point approach that modifies the MLS functional. Lagrange multipliers are used to impose a nearly exact satisfaction of the internal equilibrium equation. The numerical results show the high accuracy of the proposed error estimator.