Fully Computable a Posteriori Error Bounds for Hybridizable Discontinuous Galerkin Finite Element Approximations

@article{Ainsworth2018FullyCA,
  title={Fully Computable a Posteriori Error Bounds for Hybridizable Discontinuous Galerkin Finite Element Approximations},
  author={Mark Ainsworth and Guosheng Fu},
  journal={Journal of Scientific Computing},
  year={2018},
  volume={77},
  pages={443-466}
}
  • M. Ainsworth, G. Fu
  • Published 19 June 2017
  • Mathematics, Computer Science
  • Journal of Scientific Computing
We derive a posteriori error estimates for the hybridizable discontinuous Galerkin (HDG) methods, including both the primal and mixed formulations, for the approximation of a linear second-order elliptic problem on conforming simplicial meshes in two and three dimensions. We obtain fully computable, constant free, a posteriori error bounds on the broken energy seminorm and the HDG energy (semi)norm of the error. The estimators are also shown to provide local lower bounds for the HDG energy… 
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