Error Constants for the Semi-Discrete Galerkin Approximation of the Linear Heat Equation

Makoto Mizuguchi*, Mitsuhiro T. Nakao, Kouta Sekine, Shin’ichi Oishi

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, we propose L2(J;H01(Ω)) and L2(J; L2(Ω ) ) norm error estimates that provide the explicit values of the error constants for the semi-discrete Galerkin approximation of the linear heat equation. The derivation of these error estimates shows the convergence of the approximation to the weak solution of the linear heat equation. Furthermore, explicit values of the error constants for these estimates play an important role in the computer-assisted existential proofs of solutions to semi-linear parabolic partial differential equations. In particular, the constants provided in this paper are better than the existing constants and, in a sense, the best possible.

Original languageEnglish
Article number34
JournalJournal of Scientific Computing
Volume89
Issue number2
DOIs
Publication statusPublished - 2021 Nov
Externally publishedYes

Keywords

  • A priori error estimate
  • Best possible
  • Error constant
  • semi-discrete Galerkin approximation

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science
  • Numerical Analysis
  • Engineering(all)
  • Computational Theory and Mathematics
  • Computational Mathematics
  • Applied Mathematics

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