Report: Error estimation of recovered solution in FE analysis

TL;DR

This paper introduces an improved error estimation method for recovered solutions in finite element analysis, leveraging an SPR-type recovery technique that enhances accuracy and efficiency in adaptive mesh refinement.

Contribution

The authors develop a new SPR-based recovery technique considering equilibrium and displacement constraints, providing more accurate recovered solutions and error estimates for FE and XFEM frameworks.

Findings

Recovered solution error estimation is highly accurate at global and local levels.

The proposed method accelerates convergence in adaptive mesh refinement.

Computational cost is reduced compared to traditional h-adaptive methods.

Abstract

The recovery type error estimators introduced by Zienkiewicz and Zhu use a recovered stress field evaluated from the Finite Element (FE) solution. Their accuracy depends on the quality of the recovered field. In this sense, accurate results are obtained using recovery procedures based on the Superconvergent Patch recovery technique (SPR). These error estimators can be easily implemented and provide accurate estimates. Another important feature is that the recovered solution is of a better quality than the FE solution and can therefore be used as an enhanced solution. We have developed an SPR-type recovery technique that considers equilibrium and displacements constraints to obtain a very accurate recovered displacements field from which a recovered stress field can also be evaluated. We propose the use of these recovered fields as the standard output of the FE code instead of the raw FE solution. Techniques to quantify the error of the recovered solution are therefore needed. In this report we present an error estimation technique that accurately evaluates the error of the recovered solution both at global and local levels in the FEM and XFEM frameworks. We have also developed an h-adaptive mesh refinement strategy based on the error of the recovered solution. As the converge rate of the error of the recovered solution is higher than that of the FE one, the computational cost required to obtain a solution with a prescribed accuracy is smaller than for traditional h-adaptive processes.