G. Akrivis and S. Larsson

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

BIT Numerical Mathematics 45 (2005), 429-442.

Abstract. 
  Completely discrete numerical methods for a nonlinear elliptic-parabolic
  system, the time-dependent Joule heating problem, are introduced and
  analyzed.  The equations are discretized in space by a standard finite
  element method, and in time by combinations of rational implicit and
  explicit multistep schemes.  The schemes are linearly implicit in the sense
  that they require, at each time level, the solution of linear
  systems of equations. Optimal order error estimates are proved under the
  assumption of sufficiently regular solutions.

Georgios Akrivis,
Computer Science Department, University of Ioannina, 451 10 Ioannina,
Greece, akrivis@cs.uoi.gr 

Stig Larsson,
Department of Mathematics, Chalmers University of Technology and
G\"oteborg University, SE-412 96 G\"oteborg, Sweden,
stig@chalmers.se