Asymptotically exact a posteriori error estimators for first-order div least-squares methods in local and global L2 norm

@article{Cai2015AsymptoticallyEA,
  title={Asymptotically exact a posteriori error estimators for first-order div least-squares methods in local and global L2 norm},
  author={Zhiqiang Cai and Varis Carey and Jia-Yeong Ku and Eun-Jae Park},
  journal={Computers & Mathematics with Applications},
  year={2015},
  volume={70},
  pages={648-659}
}
A new asymptotically exact a posteriori error estimator is developed for first-order div least-squares (LS) finite element methods. Let (uh,h) be LS approximate solution for (u,=Au). Then, E=A1/2(h+Auh)0 is asymptotically exact a posteriori error estimator for A1/2(uuh)0 or A1/2(h)0 depending on the order of approximate spaces for and u. For E to be asymptotically exact for A1/2(uuh)0, we require higher order approximation property for , and vice versa. When both Au and are approximated in the… CONTINUE READING

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