An adaptive mesh refinement scheme for solidification problems

Methods for adaptive mesh refinement, based on a quadtree data structure, have been developed with the specific objective of tracking solid/liquid front movement in two-dimensional solidification problems. These methods include mesh refinement and unrefinement algorithms for the finite element method applied to transient problems. An a posteriori error estimator is described to locate regions in the finite element mesh needing refinement. One- and two-dimensional example applications are given, showing how the methods can be used to resolve a moving solidification front and its associated boundary layer in binary alloy solidification.