Numerical experiments using hierarchical finite element method for nonlinear heat conduction in plates

In this paper, we consider a nonlinear hierarchical finite element method for heat conduction problems over two- or three-dimensional plates. Problems considered are nonlinear because the heat conductivity parameter depends upon the temperature itself. This paper explores a new technique recently proposed by the first author which transforms a nonlinear parabolic problem to a linear problem at the discrete level. We present several numerical examples which demonstrate the efficiency of the current technique.