An a-posteriori error estimate for hp-adaptive DG methods for convection-diffusion problems on anisotropically refined meshes

@article{Giani2014AnAE,
  title={An a-posteriori error estimate for hp-adaptive DG methods for convection-diffusion problems on anisotropically refined meshes},
  author={Stefano Giani and Dominik Sch{\"o}tzau and Liang Zhu},
  journal={Computers & Mathematics with Applications},
  year={2014},
  volume={67},
  pages={869-887}
}
We prove an a-posteriori error estimate for hp-adaptive discontinuous Galerkin methods for the numerical solution of convection-diffusion equations on anisotropically refined rectangular elements. The estimate yields global upper and lower bounds of the errors measured in terms of a natural norm associated with diffusion and a semi-norm associated with convection. The anisotropy of the underlying meshes is incorporated in the upper bound through an alignment measure. We present a series of… CONTINUE READING
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