Numerical verification method for positive solutions of elliptic problems

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Abstract

The purpose of this paper is to propose methods for verifying the positivity of a weak solution u of an elliptic problem assuming H0 1-error estimation ‖u−uˆ‖H0 1 ≤ρ given some numerical approximation uˆ and an explicit error bound ρ. We provide a sufficient condition for the solution to be positive and analyze the range of application of our method for elliptic problems with polynomial nonlinearities. We present numerical examples where our method is applied to some important problems.

Original languageEnglish
Article number112647
JournalJournal of Computational and Applied Mathematics
Volume370
DOIs
Publication statusPublished - 2020 May 15

Keywords

  • Computer-assisted proof
  • Elliptic problems
  • Newton's method
  • Numerical verification
  • Positive solutions
  • Verified numerical computation

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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