Numerical Modeling and Open-Source Implementation of Variational Partition-of-Unity Localizations of Space-Time Dual-Weighted Residual Estimators for Parabolic Problems

In this work, we consider space-time goal-oriented a posteriori error estimation for parabolic problems. Temporal and spatial discretizations are based on Galerkin finite elements of continuous and discontinuous type. The main objectives are the development and analysis of space-time estimators, in...

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Bibliographic Details
Published inJournal of scientific computing Vol. 99; no. 1; p. 25
Main Authors Thiele, J. P., Wick, T.
Format Journal Article
LanguageEnglish
Published New York Springer US 01.04.2024
Springer Nature B.V
Subjects
Algorithms
Computational Mathematics and Numerical Analysis
Decomposition
Estimators
Mathematical analysis
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Numerical models
Partial differential equations
Random access memory
Spacetime
Theoretical
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Summary:In this work, we consider space-time goal-oriented a posteriori error estimation for parabolic problems. Temporal and spatial discretizations are based on Galerkin finite elements of continuous and discontinuous type. The main objectives are the development and analysis of space-time estimators, in which the localization is based on a weak form employing a partition-of-unity. The resulting error indicators are used for temporal and spatial adaptivity. Our developments are substantiated with several numerical examples.
ISSN:0885-7474
1573-7691
DOI:10.1007/s10915-024-02485-6