Rectangular divergence-free finite elements for axisymmetric Stokes equations

期刊论文
发表日期：

2025年10月22日

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Xuefeng Liu,
Ran Zhang,
Shangyou Zhang,
Zhimin Zhang

摘要

When the 3D axisymmetric Stokes problem is reduced to a 2D problem, we design a rectangular divergence-free finite element method where the 2D velocity is approximated by continuous $Q_{k+1,k} \times Q_{k,k+1}$ $Q_{k + 1, k} \times Q_{k, k + 1}$ polynomials and the pressure is approximated by discontinuous $Q_{k}$ $Q_{k}$ polynomials, on rectangular meshes. Such a method produces divergence-free solutions for the velocity. The stability and the optimal-order of convergence are proved for the family of finite elements. Numerical tests confirm the theory.