Galerkin method for a nonlinear parabolic–elliptic system with nonlinear mixed boundary conditions

Materials which are heated by the passage of electricity are usually modeled by a 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 conductivities and the Joule effect. A computationally attractive discretization method is analyzed and shown to yield optimal error estimates in H¹. © 1993 John Wiley & Sons, Inc.