Super-localized orthogonal decomposition for convection-dominated diffusion problems.

BIT Numer Math

Institute of Mathematics & Centre for Advanced Analytics and Predictive Sciences (CAAPS), University of Augsburg, Universitätsstr. 12a, 86159 Augsburg, Germany.

Published: August 2024

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 -norm, the Galerkin projection onto this generalized finite element space even yields -independent error bounds, 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 -robust convergence without pre-asymptotic effects even in the under-resolved regime of large mesh Péclet numbers.

Download full-text PDF

Source
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC11408411PMC
http://dx.doi.org/10.1007/s10543-024-01035-8DOI Listing

Publication Analysis

Top Keywords

super-localized orthogonal
8
orthogonal decomposition
8
convection-dominated diffusion
8
diffusion problems
8
novel multi-scale
8
multi-scale method
8
regime large
8
péclet numbers
8
decomposition convection-dominated
4
problems paper
4

Similar Publications

Want AI Summaries of new PubMed Abstracts delivered to your In-box?

Enter search terms and have AI summaries delivered each week - change queries or unsubscribe any time!