An Equilibrated a Posteriori Error Estimator for Arbitrary-Order Nédélec Elements for Magnetostatic Problems

@article{Gedicke2020AnEA,
  title={An Equilibrated a Posteriori Error Estimator for Arbitrary-Order N{\'e}d{\'e}lec Elements for Magnetostatic Problems},
  author={Joscha Gedicke and Sjoerd Geevers and Ilaria Perugia},
  journal={Journal of Scientific Computing},
  year={2020},
  volume={83}
}
We present a novel a posteriori error estimator for Nédélec elements for magnetostatic problems that is constant-free, i.e. it provides an upper bound on the error that does not involve a generic constant. The estimator is based on equilibration of the magnetic field and only involves small local problems that can be solved in parallel. Such an error estimator is already available for the lowest-degree Nédélec element (Braess and Schöberl in Math Comput 77(262):651-672, 2008) and requires… Expand

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