Stable localized orthogonal decomposition in Raviart-Thomas spaces
Abstract
This work proposes a computational multiscale method for the mixed formulation of a second-order linear elliptic equation subject to a homogeneous Neumann boundary condition, based on a stable localized orthogonal decomposition (LOD) in Raviart-Thomas finite element spaces. In the spirit of numerical homogenization, the construction provides low-dimensional coarse approximation spaces that incorporate fine-scale information from the heterogeneous coefficients by solving local patch problems on a fine mesh. The resulting numerical scheme is accompanied by a rigorous error analysis, and it is applicable beyond periodicity and scale-separation in spatial dimensions two and three. In particular, this novel realization circumvents the presence of pollution terms observed in a previous LOD construction for elliptic problems in mixed formulation. Finally, various numerical experiments are provided that demonstrate the performance of the method.
Cite
@article{arxiv.2504.18322,
title = {Stable localized orthogonal decomposition in Raviart-Thomas spaces},
author = {Patrick Henning and Hao Li and Timo Sprekeler},
journal= {arXiv preprint arXiv:2504.18322},
year = {2026}
}