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)

Abstract

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
JournalComputing
Volume94
Issue number2-4
DOIs
Publication statusPublished - 2012 Mar
Externally publishedYes

Fingerprint

A Posteriori Estimates
Parabolic Problems
Initial-boundary-value Problem
Boundary value problems
Mathematical operators
Differential equations
A Priori Estimates
Operator
Finite-dimensional Approximation
Parabolic Differential Equations
Sharp Bound
Elliptic Operator
Linear differential equation
Error Estimates
Norm
Numerical Examples
Estimate

Keywords

  • 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

Cite this

On a posteriori estimates of inverse operators for linear parabolic initial-boundary value problems. / Nakao, Mitsuhiro T.; Kinoshita, Takehiko; Kimura, Takuma.

In: Computing, Vol. 94, No. 2-4, 03.2012, p. 151-162.

Research output: Contribution to journalArticle

Nakao, Mitsuhiro T. ; Kinoshita, Takehiko ; Kimura, Takuma. / On a posteriori estimates of inverse operators for linear parabolic initial-boundary value problems. In: Computing. 2012 ; Vol. 94, No. 2-4. pp. 151-162.
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