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Super-localized orthogonal decomposition for convection-dominated diffusion problems
Citation Link: https://doi.org/10.15480/882.13402
Publikationstyp
Journal Article
Publikationsdatum
2024-08-05
Sprache
English
Enthalten in
Volume
64
Issue
3
Article Number
33
Citation
BIT Numerical Mathematics 64 (3): 33 (2024-08-05)
Publisher DOI
Scopus ID
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.
Schlagworte
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
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