AFEM-by-Equilibration

This repository showcases how adaptive finite element solvers using equilibration based a posteriori error estimates can be build. Therefore, FEniCSx [1] alongside with <a href="https://github.com/brodbeck-m/dolfinx_eqlb/tree/v1.2.0">dolfinx_eqlb</a> [2], an extension for efficient flux equilibration are used. Classical benchmarks for the Poisson problem and linear elasticity are shown. The here presented code can be used to reproduce the results in the <a href="https://arxiv.org/abs/2410.09764">related publication</a>.

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[1] Baratta, I. A. et al.: DOLFINx: The next generation FEniCS problem solving environment. preprint. (2023) doi: <a href="https://doi.org/10.5281/zenodo.10447666">10.5281/zenodo.10447666</a><br>

[2] Brodbeck, M., Bertrand, F. and Ricken, T.: dolfinx_eqlb v1.2.0. DaRUS (2024) doi: <a href="https://doi.org/10.18419/darus-4498">10.18419/darus-4498</a><br>