Bonizzoni, FrancescaFrancescaBonizzoniFreese, Jan PhilipJan PhilipFreesePeterseim, DanielDanielPeterseim2024-10-082024-10-082024-08-05BIT Numerical Mathematics 64 (3): 33 (2024-08-05)https://hdl.handle.net/11420/49424This 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.en0006-383520243Springerhttps://creativecommons.org/licenses/by/4.0/35B2565N1265N1565N30Convection-dominated diffusionMulti-scale methodNumerical homogenizationSingularly perturbedSuper-localizationNatural Sciences and Mathematics::518: Numerical AnalysisNatural Sciences and Mathematics::530: PhysicsNatural Sciences and Mathematics::519: Applied Mathematics, ProbabilitiesJournal Article10.15480/882.1340210.1007/s10543-024-01035-810.15480/882.13402Journal Article