A nodal-based finite element approximation of the Maxwell problem suitable for singular solutions

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....

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Detalles Bibliográficos
Autores: Badia, Santiago|||0000-0003-2391-4086, Codina, Ramon|||0000-0002-7412-778X
Tipo de recurso: artículo
Fecha de publicación:2009
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/6064
Acceso en línea:https://hdl.handle.net/2117/6064
Access Level:acceso abierto
Palabra clave:Numerical methods and algorithms
Electromagnetism
Maxwell's problem
Singular solutions
Finite elements
Nodal interpolations
Stabilization
Càlcul numèric
Electromagnetisme
Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica
Àrees temàtiques de la UPC::Física::Electromagnetisme
Descripción
Sumario: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.