A posteriori estimates of inverse operators for boundary value problems in linear elliptic partial differential equations

@article{Watanabe2013APE,
  title={A posteriori estimates of inverse operators for boundary value problems in linear elliptic partial differential equations},
  author={Yoshitaka Watanabe and Takehiko Kinoshita and Mitsuhiro T. Nakao},
  journal={Math. Comput.},
  year={2013},
  volume={82},
  pages={1543-1557}
}
This paper presents constructive a posteriori estimates of inverse operators for boundary value problems in linear elliptic partial differential equations (PDEs) on a bounded domain. This type of estimate plays an important role in the numerical verification of the solutions for boundary value problems in nonlinear elliptic PDEs. In general, it is not easy to obtain the a priori estimates of the operator norm for inverse elliptic operators. Even if we can obtain these estimates, they are often… 
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