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Numerical analysis of a transient eddy current axisymmetric problem involving velocity terms
Author(s) -
Bermúdez Alfredo,
Reales Carlos,
Rodríguez Rodolfo,
Salgado Pilar
Publication year - 2012
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.20670
Subject(s) - mathematics , discretization , rotational symmetry , transient (computer programming) , finite element method , eddy current , degenerate energy levels , mathematical analysis , stability (learning theory) , partial differential equation , backward euler method , numerical analysis , euler's formula , current (fluid) , space (punctuation) , geometry , physics , computer science , quantum mechanics , machine learning , thermodynamics , operating system
The aim of this article is to analyze a transient axisymmetric electromagnetic model involving velocity terms in the Ohm's law. To this end, we introduce a time‐dependent weak formulation leading to a degenerate parabolic problem and establish its well posedness.We propose a finite‐element method for space discretization and prove well posedness and error estimates. Then, we combine it with a backward Euler time discretization and prove stability and error estimates. Finally, numerical results assessing the performance of the method are reported. © 2011 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2011
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