Abstract In [Nkemzi and Jung, 2013] explicit extraction formulas for the computation of the edge flux intensity functions for the Laplacian at axisymmetric edges are presented. The present paper proposes a new adaptation for the Fourier-finite-element method for efficient numerical treatment of boundary value problems for the Poisson equation in axisymmetric domains Ω̂ ⊂ ℝ3 with edges. The novelty of the method is the use of the explicit extraction formulas for the edge flux intensity functions to define a postprocessing procedure of the finite element solutions of the reduced boundary value problems on the two-dimensional meridian of Ω̂. A priori error estimates show that the postprocessing finite element strategy exhibits optimal rate of convergence on regular meshes. Numerical experiments that validate the theoretical results are presented.

中文翻译：

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带边缘的三维轴对称域中泊松方程的傅立叶有限元方法：计算边缘通量强度函数

摘要 在 [Nkemzi 和 Jung，2013] 中，提出了用于计算轴对称边缘拉普拉斯算子边缘通量强度函数的显式提取公式。本文提出了一种新的傅立叶有限元方法，用于有效数值处理轴对称域 Ω̂ ⊂ ℝ3 中泊松方程的边值问题。该方法的新颖之处在于使用边缘通量强度函数的显式提取公式来定义Ω̂ 的二维子午线上约简边值问题的有限元解的后处理过程。先验误差估计表明后处理有限元策略在规则网格上表现出最佳收敛速度。给出了验证理论结果的数值实验。