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High‐Order Numerical Methods for Electromagnetic Induction
Author(s) -
Gleim Tobias,
Kuhl Detlef
Publication year - 2017
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201710224
Subject(s) - discretization , finite element method , convergence (economics) , benchmark (surveying) , galerkin method , mathematics , runge–kutta methods , maxwell's equations , space (punctuation) , discontinuous galerkin method , rotational symmetry , order (exchange) , mathematical analysis , computer science , numerical analysis , physics , geometry , geodesy , geography , economics , thermodynamics , finance , economic growth , operating system
The present paper establishes an axisymmetric benchmark model of a conducting loop, which implies an electromagnetic induction. Therein, the fully coupled MAXWELL equations are demonstrated in a monolithic solution strategy. This dynamic problem is solved with a high order finite element discretization using GALERKIN's method in space as well as in time. Furthermore, high order RUNGE‐KUTTA time integration methods are analyzed. Studies regarding an h error estimation and the order of convergence are examined. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)