Linearly implicit finite element methods for the time-dependent Joule heating problem (Q2583163)

The emphasis of this paper is on the time-discretisation of a model resulting form the finite element discretisation of a nonlinear parabolic equation. The proposed methods are linearly implicit, in that they require only the solution of a linear system at each time step. Stability and consistency of the fully discrete scheme are shown. One should note that these schemes are in a sense only conditionally stable, as there is a mesh-condition in order to achieve optional convergence rates.