FEniCSx Error Estimation (FEniCSx-EE)

Description

FEniCSx-EE is an open source library showing how various error estimation strategies can be implemented in the FEniCSx Project finite element solver (https://fenicsproject.org). A particular focus is on implicit hierarchical a posteriori error estimators, that usually involve solving local error problems in special finite element spaces on cells of the mesh.

FEniCSx-EE is described in the pre-print:

Hierarchical a posteriori error estimation of Bank-Weiser type in the FEniCS Project, R. Bulle, J. S. Hale, A. Lozinski, S. P. A. Bordas, F. Chouly, (https://arxiv.org/abs/2102.04360).

FEniCS-EE is compatible with the development version of the FEniCSx Project (https://github.com/FEniCS).

A version for FEniCS 2019.1.0 is available at (https://github.com/rbulle/fenics-error-estimation).

Features

FEniCS-EE currently includes implementations of the following error estimation techniques for the Poisson problem:

• Implicit residual estimator of Bank and Weiser.

Upcoming features

• Implicit residual estimator of Verfürth,

the following error estimation techniques for the incompressible elasticity problem:

• Implicit residual estimator of Khan, Powell and Silvester (https://arxiv.org/abs/1710.03328),

and the following error estimation techniques for the Stokes problem:

• Implicit residual estimator of Liao and Silvester (https://doi.org/10.1016/j.apnum.2010.05.003).

The following marking strategies:

• Maximum (bulk),
• Dörfler (equilibration).

Getting started

1. Then, clone this repository using the command:

   git clone https://github.org/jhale/fenicsx-error-estimation
   

2. We currently require a custom build of FEniCSx:

   cd docker
   ./build-images.sh
   cd ../
   ./launch-container.sh
   

3. You should now have a shell inside a container with FEniCS installed. Try out an example:

   python3 setup.py install
   cd demo/pure_dirichlet
   python3 demo_pure-dirichlet.py
   

   The resulting fields are written to the directory output/ which will be shared with the host machine. These files can be opened using Paraview.

Automated testing

We use GitHub Actions to perform automated testing. All documented demos include basic sanity checks on the results.

FAQ

TODO

Citing

Please consider citing the FEniCS-EE paper and code if you find it useful.

@misc{bulle2021hierarchical,
    title={Hierarchical a posteriori error estimation of Bank-Weiser type in the FEniCS Project},
    author={Raphaël Bulle and Jack S. Hale and Alexei Lozinski and Stéphane P. A. Bordas and Franz Chouly},
    year={2021},
    eprint={2102.04360},
    archivePrefix={arXiv},
    primaryClass={math.NA}
}

@misc{bulle_fenics-ee_2019,
      title = {{FEniCS} {Error} {Estimation} {(FEniCS-EE)}},
      author = {Bulle, Raphaël, and Hale, Jack S.},
      month = jan,
      year = {2019},
      doi = {10.6084/m9.figshare.10732421},
      keywords = {FEniCS, finite element methods, error estimation},
}

along with the appropriate general FEniCS citations.

Issues and Support

Please use the issue tracker to report any issues.

Authors (alphabetical)

License

FEniCSx-EE is free software: you can redistribute it and/or modify it under the terms of the GNU Lesser General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.

This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more details.

You should have received a copy of the GNU Lesser General Public License along with FEniCSx-EE. If not, see http://www.gnu.org/licenses/.