# 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} }

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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## 211 Citations

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