Optimal order constructive a priori error estimates for a full discrete approximation of the heat equation

Takuma Kimura, Teruya Minamoto, Mitsuhiro T. Nakao

Research output: Contribution to journalArticle

Abstract

In this paper, we consider constructive a priori error estimates for a full discrete numerical solution of parabolic initial boundary value problems. Our method is based on the finite element Galerkin method with an inter-polation in time that uses the fundamental solution for semidiscretization in space. Particularly, we present optimal order error estimates for the linear finite element in both space and time directions. These error estimates are sharper than the existing results in the sense of convergence order to exact solutions. Since the sharply constructive error estimates play an essential role in improving the efficiency of the verification costs, our results are expected to contribute to a new development of the numerical proof for parabolic problems. We also present some numerical examples which confirm that our estimates have the exactly the same order of convergence as the a posteriori errors.

Original languageEnglish
Pages (from-to)202-212
Number of pages11
JournalReliable Computing
Volume25
Publication statusPublished - 2017

Fingerprint

A Priori Error Estimates
Discrete Approximation
Heat Equation
Error Estimates
Order of Convergence
Parabolic Problems
Semidiscretization
Galerkin Finite Element Method
Fundamental Solution
Initial-boundary-value Problem
Exact Solution
Interpolate
Numerical Solution
Finite Element
Galerkin methods
Numerical Examples
Boundary value problems
Costs
Estimate
Hot Temperature

Keywords

  • Constructive a priori error estimates
  • Galerkin methods
  • Parabolic problem

ASJC Scopus subject areas

  • Software
  • Computational Mathematics
  • Applied Mathematics

Cite this

Optimal order constructive a priori error estimates for a full discrete approximation of the heat equation. / Kimura, Takuma; Minamoto, Teruya; Nakao, Mitsuhiro T.

In: Reliable Computing, Vol. 25, 2017, p. 202-212.

Research output: Contribution to journalArticle

Kimura, Takuma ; Minamoto, Teruya ; Nakao, Mitsuhiro T. / Optimal order constructive a priori error estimates for a full discrete approximation of the heat equation. In: Reliable Computing. 2017 ; Vol. 25. pp. 202-212.
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