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Fix‐point linearization schemes for nonlinear steady‐state eddy current problems
Author(s) -
Janíková E.,
Slodička M.
Publication year - 2007
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.865
Subject(s) - mathematics , linearization , nonlinear system , bounded function , partial differential equation , domain (mathematical analysis) , degenerate energy levels , convergence (economics) , boundary value problem , current (fluid) , boundary (topology) , mathematical analysis , physics , quantum mechanics , economics , thermodynamics , economic growth
We study a nonlinear degenerate partial differential equation strongly motivated by the modelling of processes in type‐II superconductors in a bounded domain along with appropriate boundary conditions. We design a robust and efficient linear approximation scheme based on fix‐point principle. We prove the convergence of approximations to a weak solution of the original problem. Some numerical experiments are presented in order to illustrate the efficiency of the proposed method. Copyright © 2007 John Wiley & Sons, Ltd.