On a posteriori estimates of inverse operators for linear parabolic initial-boundary value problems

Mitsuhiro T. Nakao, Takehiko Kinoshita, Takuma Kimura

Research output: Contribution to journalArticle

8 Citations (Scopus)


We present numerically verified a posteriori estimates of the norms of inverse operators for linear parabolic differential equations. In case that the corresponding elliptic operator is not coercive, existing methods for a priori estimates of the inverse operators are not accurate and, usually, exponentially increase in time variable. We propose a new technique for obtaining the estimates of the inverse operator by using the finite dimensional approximation and error estimates. It enables us to obtain very sharp bounds compared with a priori estimates. We will give some numerical examples which confirm the actual effectiveness of our method.

Original languageEnglish
Pages (from-to)151-162
Number of pages12
Issue number2-4
Publication statusPublished - 2012 Mar
Externally publishedYes



  • A posteriori estimates
  • Galerkin finite element methods
  • Linear parabolic equations

ASJC Scopus subject areas

  • Computer Science Applications
  • Software
  • Computational Theory and Mathematics
  • Computational Mathematics
  • Numerical Analysis
  • Theoretical Computer Science

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