A divergence-free parametric finite element method for 3D Stokes equations on curved domains
Abstract
The Stokes equations play an important role in the incompressible flow simulation. In this paper, a novel divergence-free parametric mixed finite element method is proposed for solving three-dimensional Stokes equations on domains with piecewise smooth boundaries. The flow velocity and pressure are discretized with high-order parametric Brezzi-Douglas-Marini elements and volume elements, respectively, on curved tetrahedral meshes. Utilizing the interior-penalty discontinuous Galerkin (IPDG) technique, we prove the inf-sup condition for the mixed finite element pair, and high-order optimal error estimates in the energy norm, with the help of the extension and transformation of the true solution to computational domain. Moreover, the discrete velocity is exactly divergence-free, meaning that div uh = 0 holds in the curved computational domain. Numerical experiments are conducted to support the theoretical analyses.
Keywords
Cite
@article{arxiv.2512.16216,
title = {A divergence-free parametric finite element method for 3D Stokes equations on curved domains},
author = {Lingxiao Li and Haiyan Su and He Zhang and Weiying Zheng},
journal= {arXiv preprint arXiv:2512.16216},
year = {2025}
}