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.

Location
Deutsche Nationalbibliothek Frankfurt am Main
Extent
Online-Ressource
Language
Englisch

Bibliographic citation
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)

Creator

DOI
10.1515/cmam-2023-0040
URN
urn:nbn:de:101:1-2407021541281.194927505944
Rights
Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
Last update
14.08.2025, 10:57 AM CEST

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