Adaptive finite element methods based on flux and stress equilibration using FEniCSx

TL;DR

This paper demonstrates the implementation of flux and stress equilibration-based a-posteriori error estimators in FEniCSx, enhancing adaptive finite element methods for Poisson and elasticity problems.

Contribution

It introduces the dolfinx_eqlb library and details its algorithmic structure for implementing equilibrated flux estimators in FEniCSx.

Findings

Successful implementation of error estimators in FEniCSx

Improved adaptive solution procedures demonstrated on benchmarks

Applicability to Poisson and linear elasticity problems

Abstract

This contribution shows how a-posteriori error estimators based on equilibrated fluxes - H(div) functions fulfilling the underlying conservation law - can be implemented in FEniCSx. Therefore, dolfinx_eqlb is introduced, its algorithmic structure is described and classical benchmarks for adaptive solution procedures for the Poisson problem and linear elasticity are presented.