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....
| Autores: | , |
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| 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 |
| 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. |
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