  A new approach is developed for computational modelling of microstructure
evolution problems. The approach combines the phase-field method with the
recently-developed laminated element technique (LET) which is a simple and
efficient method to model weak discontinuities using nonconforming
finite-element meshes. The essence of LET is in treating the elements that are
cut by an interface as simple laminates of the two phases, and this idea is
here extended to propagating interfaces so that the volume fraction of the
phases and the lamination orientation vary accordingly. In the proposed LET-PF
approach, the phase-field variable (order parameter), which is governed by an
evolution equation of the Ginzburg-Landau type, plays the role of a level-set
function that implicitly defines the position of the (sharp) interface. The
mechanical equilibrium subproblem is then solved using the semisharp LET
technique. Performance of LET-PF is illustrated by numerical examples. In
particular, it is shown that, for the problems studied, LET-PF exhibits higher
accuracy than the conventional phase-field method so that, for instance,
qualitatively correct results can be obtained using a significantly coarser
mesh, and thus at a lower computational cost.
