{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,23]],"date-time":"2026-03-23T11:02:07Z","timestamp":1774263727000,"version":"3.50.1"},"reference-count":52,"publisher":"Walter de Gruyter GmbH","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2020,6,25]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>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 <jats:italic>\u03a9\u0302<\/jats:italic> \u2282 \u211d<jats:sup>3<\/jats:sup> 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 <jats:italic>\u03a9\u0302<\/jats:italic>. 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.<\/jats:p>","DOI":"10.1515\/jnma-2019-0002","type":"journal-article","created":{"date-parts":[[2019,6,29]],"date-time":"2019-06-29T09:06:16Z","timestamp":1561799176000},"page":"75-98","source":"Crossref","is-referenced-by-count":7,"title":["The Fourier-finite-element method for Poisson\u2019s equation in three-dimensional axisymmetric domains with edges: Computing the edge flux intensity functions"],"prefix":"10.1515","volume":"28","author":[{"given":"Boniface","family":"Nkemzi","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Science, University of Buea, Buea, Cameroon"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Michael","family":"Jung","sequence":"additional","affiliation":[{"name":"Hochschule f\u00fcr Technik und Wirtschaft Dresden, Fakult\u00e4t f\u00fcr Informatik\/Mathematik, Friedrich-List-Platz 1, 01069, Dresden, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","reference":[{"key":"ref01","volume-title":"Spectral Methods for Axisymmetric Domains","year":"1999"},{"key":"ref371","doi-asserted-by":"crossref","first-page":"837","DOI":"10.1002\/mma.1670161202","article-title":"Singularity functions at axisymmetric edges and their representation by Fourier series","volume":"16","year":"1993","journal-title":"Math. 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