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Analysis of an unconditionally convergent stabilized finite element formulation for incompressible magnetohydrodynamics
Badia, Santiago; Codina, Ramon; Planas Badenas, 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
In this work, we analyze a recently proposed stabilized finite element formulation for the approximation of the resistive magnetohydrodynamics equations. The novelty of this formulation with respect to existing ones is the fact that it always converges to the physical solution, even when it is singular. We have performed a detailed stability and convergence analysis of the formulation in a simplified setting. From the convergence analysis, we infer that a particular type of meshes with a macro-element structure is needed, which can be easily obtained after a straight modification of any original mesh.
Àrees temàtiques de la UPC::Física::Física de fluids
Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Mètodes en elements finits
Magnetohydrodynamics--Mathematical models
magnetohydrodynamics
finite elements
singular solutions
stabilized finite element methods
Magnetohidrodinàmica -- Models matemàtics
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