Computational Multiscale Methods for Nondivergence-Form Elliptic Partial Differential Equations

to related objects

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: Freese, Philip
Gallistl, Dietmar
Peterseim, Daniel
Sprekeler, Timo

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

Data provider

This object is provided by:
Deutsche Nationalbibliothek. If you have any questions about the object, please contact the data provider.

Show original at data provider

Associated

Other Objects (12)

Computational multiscale methods for nondivergence-form elliptic partial differential equations

Computational multiscale methods for nondivergence-form elliptic partial differential equations

Computational multiscale methods for nondivergence-form elliptic partial differential equations

Computational multiscale methods for nondivergence-form elliptic partial differential equations

Robust numerical upscaling of elliptic multiscale problems at high contrast

Robust numerical upscaling of elliptic multiscale problems at high contrast

Localization of elliptic multiscale problems

Localization of elliptic multiscale problems

Super-localization of elliptic multiscale problems

Super-localization of elliptic multiscale problems

Finite element discretization of multiscale elliptic problems

Finite element discretization of multiscale elliptic problems

Variational multiscale stabilization and the exponential decay of fine-scale correctors

Variational multiscale stabilization and the exponential decay of fine-scale correctors

Robust numerical upscaling of elliptic multiscale problems at high contrast

Robust numerical upscaling of elliptic multiscale problems at high contrast

Composite finite elements for elliptic interface problems

Composite finite elements for elliptic interface problems

A multiscale method for porous microstructures

A multiscale method for porous microstructures

Computational multiscale methods: introduction by the organisers

Computational multiscale methods: introduction by the organisers

Computation of local and quasi-local effective diffusion tensors in elliptic homogenization

Computation of local and quasi-local effective diffusion tensors in elliptic homogenization

Computational multiscale methods for nondivergence-form elliptic partial differential equations

Computational multiscale methods for nondivergence-form elliptic partial differential equations

Computational multiscale methods for nondivergence-form elliptic partial differential equations

Computational multiscale methods for nondivergence-form elliptic partial differential equations

Robust numerical upscaling of elliptic multiscale problems at high contrast

Robust numerical upscaling of elliptic multiscale problems at high contrast

Localization of elliptic multiscale problems

Localization of elliptic multiscale problems

Super-localization of elliptic multiscale problems

Super-localization of elliptic multiscale problems

Finite element discretization of multiscale elliptic problems

Finite element discretization of multiscale elliptic problems

Variational multiscale stabilization and the exponential decay of fine-scale correctors

Variational multiscale stabilization and the exponential decay of fine-scale correctors

Robust numerical upscaling of elliptic multiscale problems at high contrast

Robust numerical upscaling of elliptic multiscale problems at high contrast

Composite finite elements for elliptic interface problems

Composite finite elements for elliptic interface problems

A multiscale method for porous microstructures

A multiscale method for porous microstructures

Computational multiscale methods: introduction by the organisers

Computational multiscale methods: introduction by the organisers

Computation of local and quasi-local effective diffusion tensors in elliptic homogenization

Computation of local and quasi-local effective diffusion tensors in elliptic homogenization

Computational multiscale methods for nondivergence-form elliptic partial differential equations

Computational multiscale methods for nondivergence-form elliptic partial differential equations

Computational multiscale methods for nondivergence-form elliptic partial differential equations

Computational multiscale methods for nondivergence-form elliptic partial differential equations

Robust numerical upscaling of elliptic multiscale problems at high contrast

Robust numerical upscaling of elliptic multiscale problems at high contrast

Localization of elliptic multiscale problems

Localization of elliptic multiscale problems

Super-localization of elliptic multiscale problems

Super-localization of elliptic multiscale problems

Finite element discretization of multiscale elliptic problems

Finite element discretization of multiscale elliptic problems

Variational multiscale stabilization and the exponential decay of fine-scale correctors

Variational multiscale stabilization and the exponential decay of fine-scale correctors

Robust numerical upscaling of elliptic multiscale problems at high contrast

Robust numerical upscaling of elliptic multiscale problems at high contrast

Composite finite elements for elliptic interface problems

Composite finite elements for elliptic interface problems

A multiscale method for porous microstructures

A multiscale method for porous microstructures

Computational multiscale methods: introduction by the organisers

Computational multiscale methods: introduction by the organisers

Computation of local and quasi-local effective diffusion tensors in elliptic homogenization

Computation of local and quasi-local effective diffusion tensors in elliptic homogenization

Cultural heritage institutions wishing to register will find more information here.

Fields marked * need to be filled in.

Username*

Please enter your username

Email*

Please enter your email address

Please do not fill this field

First name

Last name

Password*

Please enter your password

Confirm password*

Please enter the same password

I have read the terms of use and the privacy policy for the collection of personal data and accept them. *

This field is required.

I would like to subscribe to the newsletter of the Deutsche Digitale Bibliothek. See newsletter subscription info.

Account created

Your "My DDB" account has been successfully created. Before you can log in to your account, you must click the confirmation link in the message we just sent to the email address you provided.