Induction hardening of steel with restrained joule heating and nonlinear law for magnetic induction field: solvability

DOI10.1016/j.cam.2016.08.016zbMath1352.35069OpenAlexW2518890063MaRDI QIDQ730593

Marián Slodička, Jaroslav Chovan

Publication date: 28 December 2016

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2016.08.016

zbMATH Keywords

Maxwell's equationsmonotone operatorsRothe's methodJoule heatinginduction hardening

Mathematics Subject Classification ID

Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Nonlinear initial, boundary and initial-boundary value problems for nonlinear parabolic equations (35K61) Maxwell equations (35Q61) PDEs in connection with classical thermodynamics and heat transfer (35Q79)

Related Items (5)

The solvability of coupling the thermal effect and magnetohydrodynamics field with turbulent convection zone and the flow field ⋮ Solvability of wave propagation with Debye polarization in nonlinear dielectric materials and its finite element methods approximation ⋮ Model recovery for Hammerstein systems using the hierarchical orthogonal matching pursuit method ⋮ \(A\)-\(\phi\) formulation of a mathematical model for the induction hardening process with a nonlinear law for the magnetic field ⋮ Existence of a weak solution to a nonlinear induction hardening problem with Leblond-Devaux model for a steel workpiece

Uses Software

• MaxFEM

Cites Work

• Optimal error analysis of Galerkin FEMs for nonlinear Joule heating equations
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• Global solutions of the non-linear problem describing Joule's heating in three space dimensions
• A time discretization scheme for a non-linear degenerate eddy current model for ferromagnetic materials
• UNIFORM BMO ESTIMATE OF PARABOLIC EQUATIONS AND GLOBAL WELL-POSEDNESS OF THE THERMISTOR PROBLEM
• Global solutions of Maxwell's equations in an electromagnetic field with a temperature-dependent electrical conductivity
• Modelling of continual induction hardening in quasi‐coupled formulation
• Finite Element Methods for Maxwell's Equations
• A Finite Element Model for the Time-Dependent Joule Heating Problem
• Mathematical Models and Numerical Simulation in Electromagnetism
• Nonlinear partial differential equations with applications
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