Publication

A quasi-static two-dimensional induction heating problem II. Numerical analysis

Jacques Rappaz, Catherine Parietti
1999
Journal Articles

Abstract

We consider a nonlinear elliptic-parabolic system which stems from the modelling of heat induction processes in which a sinusoidal electromagnetic field is applied at the boundary of the inductor. The magnetic field satisfies an elliptic equation whereas the temperature equation is parabolic. These two equations are coupled due to the Joule effect and to the conductivity dependence on temperature. A Galerkin method for our problem is analyzed and shown to yield error estimates in L-2 and H-1.

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https://infoscience.epfl.ch/entities/publication/500566f6-1f7c-4a4d-a104-dde2a97e27de

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Jacques Rappaz, Catherine Parietti
1999
Journal Articles

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/500566f6-1f7c-4a4d-a104-dde2a97e27de

About this result

Related concepts (32)

Elliptic partial differential equation

Second-order linear partial differential equations (PDEs) are classified as either elliptic, hyperbolic, or parabolic. Any second-order linear PDE in two variables can be written in the form where A, B, C, D, E, F, and G are functions of x and y and where , and similarly for . A PDE written in this form is elliptic if with this naming convention inspired by the equation for a planar ellipse.

Elliptic operator

In the theory of partial differential equations, elliptic operators are differential operators that generalize the Laplace operator. They are defined by the condition that the coefficients of the highest-order derivatives be positive, which implies the key property that the principal symbol is invertible, or equivalently that there are no real characteristic directions. Elliptic operators are typical of potential theory, and they appear frequently in electrostatics and continuum mechanics.

Magnetic field

A magnetic field is a vector field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular to its own velocity and to the magnetic field. A permanent magnet's magnetic field pulls on ferromagnetic materials such as iron, and attracts or repels other magnets.

Related publications (32)

A quasi-static two-dimensional induction heating problem II. Numerical analysis

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