Improvement of the Constructive A Priori Error Estimates for a Fully Discretized Periodic Solution of Heat Equation

In this study, we present new sharper constructive a priori error estimates for a full-discrete numerical solution of the heat equation that refines our previous work. The full discretization is given using the finite element method in space and linear interpolation in time, similar to that in the p...

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Bibliographic Details
Published inJournal of computational methods in applied mathematics Vol. 22; no. 3; pp. 631 - 647
Main Authors Kimura, Takuma, Minamoto, Teruya, Nakao, Mitsuhiro T.
Format Journal Article
LanguageEnglish
Published Minsk De Gruyter 01.07.2022
Walter de Gruyter GmbH
Subjects
35B10
35K05
65M15
65M60
Constructive A Priori Error Estimates
Discretization
Estimates
Finite Element Method
Interpolation
Parabolic Problem
Periodic Solutions
Thermodynamics
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Summary:In this study, we present new sharper constructive a priori error estimates for a full-discrete numerical solution of the heat equation that refines our previous work. The full discretization is given using the finite element method in space and linear interpolation in time, similar to that in the previous work. In particular, we adopt an approach based on the effective use of the properties both for exact and discretized time-periodic solutions to establish the error estimates simpler and sharper than the previous work. Furthermore, we derive some time-stepwise error estimates in the space direction. Finally, we present several numerical examples that confirm the actual refinements of the convergence.
ISSN:1609-4840
1609-9389
DOI:10.1515/cmam-2022-0015