Computational Multiscale Methods for Nondivergence-Form Elliptic Partial Differential Equations

Abstract: 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.

Standort
Deutsche Nationalbibliothek Frankfurt am Main
Umfang
Online-Ressource
Sprache
Englisch

Erschienen in
Computational Multiscale Methods for Nondivergence-Form Elliptic Partial Differential Equations ; volume:24 ; number:3 ; year:2024 ; pages:649-672 ; extent:24
Computational methods in applied mathematics ; 24, Heft 3 (2024), 649-672 (gesamt 24)

Urheber

DOI
10.1515/cmam-2023-0040
URN
urn:nbn:de:101:1-2407021541281.194927505944
Rechteinformation
Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
Letzte Aktualisierung
14.08.2025, 10:57 MESZ

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