Numerical analysis of coupled nonlinear partial differential equations modelling electro-thermal applications
Materials which are heated by the passage of electricity are usually modeled by nonlinear coupled system of two partial differential equations. The current equation is elliptic, while the temperature equation is parabolic. These equations are coupled one to another through the temperature dependence in the conductivities and the Joule effect of electric resistance. Two finite element procedures are introduced to approximate the temperature and the electric potential. The temperature is treated by a Galerkin method, then by a mixed method. An optimal time stepping scheme for the Galerkin method is discussed, and an optimal error estimate is derived for the mixed procedure. The time stepping scheme yields a linear system at each time step, thereby avoiding the solution of nonlinear systems. Numerical results based on the Galerkin method are presented for differential equations with various degrees of nonlinearities.
- Research Organization:
- Pittsburgh Univ., PA (United States)
- OSTI ID:
- 7206893
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
420400 -- Engineering-- Heat Transfer & Fluid Flow
661300* -- Other Aspects of Physical Science-- (1992-)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
CALCULATION METHODS
DIFFERENTIAL EQUATIONS
ELECTRIC HEATING
ELECTRICITY
EQUATIONS
FINITE ELEMENT METHOD
GALERKIN-PETROV METHOD
HEATING
ITERATIVE METHODS
JOULE HEATING
NONLINEAR PROBLEMS
NUMERICAL SOLUTION
PARTIAL DIFFERENTIAL EQUATIONS
PLASMA HEATING
RESISTANCE HEATING
THERMOELECTRICITY