Super-localized orthogonal decomposition for convection-dominated diffusion problems

• Published in: BIT Vol. 64; no. 3; p. 33
• Main Authors: Bonizzoni, Francesca, Freese, Philip, Peterseim, Daniel
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.09.2024; Springer Nature B.V
• Subjects: Asymptotic methods; Computational Mathematics and Numerical Analysis; Convection; Decomposition; Error analysis; Mathematics; Mathematics and Statistics; Multiscale analysis; Numeric Computing; Peclet number; Research Paper; Singular perturbation; 65N15; 65N12; 35B25; Multi-scale method; Convection-dominated diffusion; Numerical homogenization; Singularly perturbed; Super-localization; 65N30
• ISSN: 0006-3835; 1572-9125; 1572-9125
• DOI: 10.1007/s10543-024-01035-8

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 sp...