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

2024/10/13 by Brodbeck, Maximilian, Bertrand, Fleurianne, Ricken, Tim
#FOS: Computer and information sciences #FOS: Mathematics #Mathematical Software (cs.MS) #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2410.09764

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.

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