• DOI:10.1137/S003614290139874X
• Corpus ID: 5220418

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 $\nabla u$. Here Qh is the global L2 projection. In Part II, we analyze a superconvergent gradient recovery scheme for general unstructured, shape regular triangulations. This is the foundation for an a posteriori error estimate and local error indicators.