A numerical approach to the proof of existence of solutions for elliptic problems

@article{Nakao1988ANA,
  title={A numerical approach to the proof of existence of solutions for elliptic problems},
  author={Mitsuhiro T. Nakao},
  journal={Japan Journal of Applied Mathematics},
  year={1988},
  volume={5},
  pages={313-332}
}
  • M. Nakao
  • Published 1 November 1988
  • Mathematics
  • Japan Journal of Applied Mathematics
In this paper, we describe a method which proves by computers the existence of weak solutions for linear elliptic boundary value problems of second order. It is shown that we can constitute the computing procedures to verify the existence, uniqueness and inclusion set of a solution based on Schauder’s fixed point theorem. Using the finite element approximations for some simple Poisson’s equations and the results of error estimates, we generate iteratively a set sequence composed of functions… 
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