Pressure-Robust Fortin-Soulie Elements of the Stokes Equation on Curved Domains

Wei Chen; Zhen Liu

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arXiv · 2604.12769

Pressure-Robust Fortin-Soulie Elements of the Stokes Equation on Curved Domains

Wei Chen·Zhen Liu

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Abstract

This paper presents a pressure-robust and element-wise divergence-free nonconforming finite element method for the Stokes problem on curved domains. The discrete element is constructed by mapping the Fortin-Soulie element from a reference triangle using an isoparametric mapping for the geometry and a Piola transform for the function space. The inf-sup condition and the error estimate with optimal convergence rate are proved. Pressure-robustness is obtained by replacing the discrete velocity test functions with the first-order Raviart-Thomas functions. Numerical examples are provided to validate the theoretical results.

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Wei Chen, Zhen Liu. 2026-04-14. Pressure-Robust Fortin-Soulie Elements of the Stokes Equation on Curved Domains. https://arxiv.org/abs/2604.12769

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