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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 dels Materials i Estructures en Enginyeria; Universitat Politècnica de Catalunya. (MC)2 - Grup de Mecànica Computacional en Medis Continus
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.
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
Attribution-NonCommercial-NoDerivs 3.0 Spain
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
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