Computational multiscale methods for nondivergence-form elliptic partial differential equations

  • 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.

Download full text files

Export metadata


Number of document requests

Additional Services

Share in Twitter Search Google Scholar
Author:Philip Freese, Dietmar Gallistl, Daniel PeterseimORCiDGND, Timo Sprekeler
Frontdoor URL
Parent Title (English):Computational Methods in Applied Mathematics
Publisher:Walter de Gruyter
Place of publication:Berlin
Year of first Publication:2023
Publishing Institution:Universität Augsburg
Release Date:2023/08/31
Tag:Applied Mathematics; Computational Mathematics; Numerical Analysis
Institutes:Mathematisch-Naturwissenschaftlich-Technische Fakultät
Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik
Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik / Lehrstuhl für Numerische Mathematik
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
Latest Publications (not yet published in print):Aktuelle Publikationen (noch nicht gedruckt erschienen)
Licence (German):CC-BY 4.0: Creative Commons: Namensnennung (mit Print on Demand)