I will present a phase field approximation for sharp interface energies, defined
on partitions, as appropriate for modeling grain boundaries in polycrystals. The
label takes value in O(d)/G, where G is the point group of a lattice, the phase-
field approximation fully respects the symmetry. These functionals can be used
for the simulation of grain growth or for image reconstruction of grain bound-
aries. A suitable discretization scheme based on multivalued finite elements
will then be discussed.
The talk is based on joint work with Vito Crismale, Adriana Garroni and
Annalisa Malusa (Sapienza, Roma)