Optimal a priori error estimates for the hp-version of the local discontinuous Galerkin method for convection-diffusion problems

@article{Castillo2002OptimalAP,
  title={Optimal a priori error estimates for the hp-version of the local discontinuous Galerkin method for convection-diffusion problems},
  author={Paul Castillo and Bernardo Cockburn and Dominik Sch{\"o}tzau and Christoph Schwab},
  journal={Math. Comput.},
  year={2002},
  volume={71},
  pages={455-478}
}
We study the convergence properties of the hp-version of the local discontinuous Galerkin finite element method for convection-diffusion problems; we consider a model problem in a one-dimensional space domain. We allow arbitrary meshes and polynomial degree distributions and obtain upper bounds for the energy norm of the error which are explicit in the mesh-width h, in the polynomial degree p, and in the regularity of the exact solution. We identify a special numerical flux for which the… CONTINUE READING