Discontinuous Galerkin Methods for Advection-Diffusion-Reaction Problems on Anisotropically Refined Meshes

@article{Georgoulis2007DiscontinuousGM,
  title={Discontinuous Galerkin Methods for Advection-Diffusion-Reaction Problems on Anisotropically Refined Meshes},
  author={Emmanuil H. Georgoulis and Edward J. C. Hall and Paul Houston},
  journal={SIAM J. Scientific Computing},
  year={2007},
  volume={30},
  pages={246-271}
}
In this paper we consider the a posteriori and a priori error analysis of discontinuous Galerkin interior penalty methods for second–order partial differential equations with nonnegative characteristic form on anisotropically refined computational meshes. In particular, we discuss the question of error estimation for linear target functionals, such as the outflow flux and the local average of the solution. Based on our a posteriori error bound we design and implement the corresponding adaptive… CONTINUE READING

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