Super-localized orthogonal decomposition for convection-dominated diffusion problems

Publikationstyp
Journal Article
Date Issued
2024-08-05
Sprache
English
Author(s)
Bonizzoni, Francesca  
Freese, Jan Philip  orcid-logo
Mathematik E-10  
Peterseim, Daniel  
TORE-DOI
10.15480/882.13402
TORE-URI
https://hdl.handle.net/11420/49424
Journal
BIT  
Volume
64
Issue
3
Article Number
33
Citation
BIT Numerical Mathematics 64 (3): 33 (2024)
Publisher DOI
10.1007/s10543-024-01035-8
Scopus ID
2-s2.0-85200492897
Publisher
Springer
This paper presents a novel multi-scale method for convection-dominated diffusion problems in the regime of large Péclet numbers. The method involves applying the solution operator to piecewise constant right-hand sides on an arbitrary coarse mesh, which defines a finite-dimensional coarse ansatz space with favorable approximation properties. For some relevant error measures, including the L2-norm, the Galerkin projection onto this generalized finite element space even yields ε-independent error bounds, ε being the singular perturbation parameter. By constructing an approximate local basis, the approach becomes a novel multi-scale method in the spirit of the Super-Localized Orthogonal Decomposition (SLOD). The error caused by basis localization can be estimated in an a posteriori way. In contrast to existing multi-scale methods, numerical experiments indicate ε-robust convergence without pre-asymptotic effects even in the under-resolved regime of large mesh Péclet numbers.
Subjects
35B25
65N12
65N15
65N30
Convection-dominated diffusion
Multi-scale method
Numerical homogenization
Singularly perturbed
Super-localization
DDC Class
518: Numerical Analysis
530: Physics
519: Applied Mathematics, Probabilities
Publication version
publishedVersion
Lizenz
https://creativecommons.org/licenses/by/4.0/
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