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Computational multiscale methods for nondivergence-form elliptic partial differential equations

Citation Link: https://doi.org/10.15480/882.8261
Publikationstyp
Journal Article
Date Issued
2024-07-01
Sprache
English
Author(s)
Freese, Jan Philip  orcid-logo
Mathematik E-10  
Gallistl, Dietmar  
Peterseim, Daniel  
Sprekeler, Timo  
TORE-DOI
10.15480/882.8261
TORE-URI
https://hdl.handle.net/11420/42796
Journal
Computational methods in applied mathematics  
Volume
24
Issue
3
Start Page
649
End Page
672
Citation
Computational Methods in Applied Mathematics 24 (3): 649-672 (2024)
Publisher DOI
10.1515/cmam-2023-0040
Scopus ID
2-s2.0-85163829477
This paper proposes novel computational multiscale methods for linear second-order elliptic partial differential equations in nondivergence form with heterogeneous coefficients satisfying a Cordes condition. The construction follows the methodology of localized orthogonal decomposition (LOD) and provides operator-adapted coarse spaces by solving localized cell problems on a fine scale in the spirit of numerical homogenization. The degrees of freedom of the coarse spaces are related to nonconforming and mixed finite element methods for homogeneous problems. The rigorous error analysis of one exemplary approach shows that the favorable properties of the LOD methodology known from divergence-form PDEs, i.e., its applicability and accuracy beyond scale separation and periodicity, remain valid for problems in nondivergence form.
Subjects
Finite Element Methods
Localized Orthogonal Decomposition
Nondivergence-Form Elliptic PDE
Numerical Homogenization
DDC Class
510: Mathematics
Publication version
publishedVersion
Lizenz
https://creativecommons.org/licenses/by/4.0/
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