2026-04-13T02:39:43Zhttps://recercat.cat/oai/request

oai:recercat.cat:2117/60642025-07-17T06:06:46Zcom_2072_1033col_2072_452950

A nodal-based finite element approximation of the Maxwell problem suitable for singular solutions Badia, Santiago Codina, Ramon Universitat Politècnica de Catalunya. Departament de Resistència de Materials i Estructures a l'Enginyeria Universitat Politècnica de Catalunya. (MC)2 - Grup de Mecànica Computacional en Medis Continus Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica Àrees temàtiques de la UPC::Física::Electromagnetisme Numerical methods and algorithms Electromagnetism Maxwell's problem Singular solutions Finite elements Nodal interpolations Stabilization Càlcul numèric Electromagnetisme A new mixed finite element approximation of Maxwell’s problem is proposed, its main features being that it is based on a novel augmented formulation of the continuous problem and the introduction of a mesh dependent stabilizing term, which yields a very weak control on the divergence of the unknown. The method is shown to be stable and convergent in the natural H (curl; Ω) norm for this unknown. In particular, convergence also applies to singular solutions, for which classical nodal based interpolations are known to suffer from spurious convergence upon mesh refinement. 2009-11-17 Article https://hdl.handle.net/2117/6064 eng info:eu-repo/grantAgreement/EC/FP7/258443/EU/Computational Methods for Fusion Technology/COMFUS http://creativecommons.org/licenses/by-nc-nd/3.0/es/ Open Access Attribution-NonCommercial-NoDerivs 3.0 Spain 20 p. application/pdf