Local projection stabilization methods for $\boldsymbol{H}({\rm curl})$ and $\boldsymbol{H}({\rm div})$ advection problems
Numerical Analysis
2025-05-23 v1 Numerical Analysis
Abstract
We devise local projection stabilization (LPS) methods for advection problems in the (curl) and (div) spaces, employing conforming finite element spaces of arbitrary order within a unified framework. The key ingredient is a local inf-sup condition, enabled by enriching the approximation space with appropriate (d) bubble functions (with d = curl or div). This enrichment allows for the construction of modified interpolation operators, which are crucial for establishing optimal a priori error estimates in the energy norm. Numerical examples are presented to verify both the theoretical results and the stabilization properties of the proposed method.
Keywords
Cite
@article{arxiv.2505.16468,
title = {Local projection stabilization methods for $\boldsymbol{H}({\rm curl})$ and $\boldsymbol{H}({\rm div})$ advection problems},
author = {Yangfan Luo and Jindong Wang and Shuonan Wu},
journal= {arXiv preprint arXiv:2505.16468},
year = {2025}
}