A Priori and a Posteriori Error Estimates of a WOPSIP DG Method for the Heat Equation

We introduce and analyze a weakly overpenalized symmetric interior penalty method for solving the heat equation. We first provide optimal a priori error estimates in the energy norm for the fully discrete scheme with backward Euler time-stepping. In addition, we apply elliptic reconstruction techniq...

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Bibliographic Details
Published inMathematical problems in engineering Vol. 2020; no. 2020; pp. 1 - 11
Main Authors Zhu, Huijian, Liang, Fen, Wen, Kun-Wen, Zeng, Yuping
Format Journal Article
LanguageEnglish
Published Cairo, Egypt Hindawi Publishing Corporation 2020
Hindawi
Hindawi Limited
Subjects
Adaptive algorithms
Error analysis
Errors
Estimates
Inequality
Methods
Thermodynamics
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Summary:We introduce and analyze a weakly overpenalized symmetric interior penalty method for solving the heat equation. We first provide optimal a priori error estimates in the energy norm for the fully discrete scheme with backward Euler time-stepping. In addition, we apply elliptic reconstruction techniques to derive a posteriori error estimators, which can be used to design adaptive algorithms. Finally, we present two numerical experiments to validate our theoretical analysis.
ISSN:1024-123X
1563-5147
DOI:10.1155/2020/7525676