Uniform norm error estimate for rectangular finite element approximation of a 2D turning point problem
Numerical Analysis
2026-02-09 v2 Numerical Analysis
Abstract
This work presents error analysis for a finite element method applied to a two-dimensional singularly perturbed convection-diffusion turning point problem. Utilizing a layer-adapted Shishkin mesh, we prove uniform convergence in the maximum norm in the x-layer regions and -independent bounds for the coarse region. The analysis, critically based on the properties of a discrete Green's function, guarantees the method's robustness and accuracy in capturing sharp solution layers.
Cite
@article{arxiv.2512.01841,
title = {Uniform norm error estimate for rectangular finite element approximation of a 2D turning point problem},
author = {Shallu and Sudipto Chowdhury and Vikas Gupta},
journal= {arXiv preprint arXiv:2512.01841},
year = {2026}
}