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The Fourier-finite-element method for Poisson’s equation in three-dimensional axisymmetric domains with edges: Computing the edge flux intensity functions

Boniface Nkemzi and Michael Jung

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.

JEL Classification: 35J05; 35J25; 65N30; 65N35; 65N15

Acknowledgment

This work was done while the author B. Nkemzi was visiting the University of Applied Sciences, Dresden, Germany for a short research stay. His visit was supported by the Alexander von Humboldt Foundation, Bonn, Germany in his capacity as an Alexander von Humboldt Alumnus. Boniface Nkemzi is very grateful for the support and also expresses his sincere thanks to the staff of the Faculty of Computer Science and Mathematics for their warm hospitality during his stay. Our sincere thanks go also to the anonymous reviewers who gave us very useful suggestions that led to a significant improvement of the original article.

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Received: 2019-01-03
Revised: 2019-05-21
Accepted: 2019-06-06
Published Online: 2019-06-29
Published in Print: 2020-06-25

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