Asymptotically Exact A Posteriori Error Estimators, Part I: Grids with Superconvergence

@article{Bank2003AsymptoticallyEA,
  title={Asymptotically Exact A Posteriori Error Estimators, Part I: Grids with Superconvergence},
  author={Randolph E. Bank and Jinchao Xu},
  journal={SIAM J. Numer. Anal.},
  year={2003},
  volume={41},
  pages={2294-2312}
}
  • R. Bank, Jinchao Xu
  • Published 1 June 2003
  • Computer Science, Mathematics
  • SIAM J. Numer. Anal.
In Part I of this work, we develop superconvergence estimates for piecewise linear finite element approximations on quasi-uniform triangular meshes where most pairs of triangles sharing a common edge form approximate parallelograms. In particular, we first show a superconvergence of the gradient of the finite element solution uh and to the gradient of the interpolant uI. We then analyze a postprocessing gradient recovery scheme, showing that $Q_h\nabla u_h$ is a superconvergent approximation to… 

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