A posteriori error estimates and resulting adaptive finite element schemes allow for the determination of solutions with predefined accuracy while preserving optimal convergence orders. An important class of guaranteed, robust error upper bounds, mostly in the energy norm, are based on so-called equilibrated fluxes. This contribution shows how such fluxes – H(div) functions fulfilling the problems underlying conservation law – can be calculated in FEniCSx. The introduction of dolfinx_eqlb and its algorithmic structure are thus described, and classical benchmarks for adaptive solution procedures for the Poisson problem and linear elasticity are presented.

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Adaptive Finite Element Methods Based on Flux Equilibration Using FEniCSx

  • Maximilian Brodbeck,
  • Fleurianne Bertrand,
  • Tim Ricken

摘要

A posteriori error estimates and resulting adaptive finite element schemes allow for the determination of solutions with predefined accuracy while preserving optimal convergence orders. An important class of guaranteed, robust error upper bounds, mostly in the energy norm, are based on so-called equilibrated fluxes. This contribution shows how such fluxes – H(div) functions fulfilling the problems underlying conservation law – can be calculated in FEniCSx. The introduction of dolfinx_eqlb and its algorithmic structure are thus described, and classical benchmarks for adaptive solution procedures for the Poisson problem and linear elasticity are presented.