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arXiv · 2512.01841

Uniform norm error estimate for rectangular finite element approximation of a 2D turning point problem

Shallu·Sudipto Chowdhury·Vikas Gupta
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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 $\varepsilon$-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.

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Shallu, Sudipto Chowdhury, Vikas Gupta. 2025-12-01. Uniform norm error estimate for rectangular finite element approximation of a 2D turning point problem. https://arxiv.org/abs/2512.01841

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