A variational approach to two dimensional grain growth-I. Theory

A variational approach to modelling two-dimensional grain-growth is presented. This variational principle provides the basis for a numerical scheme which uses a cubic polynomial shape function to represent the shape of a grain-boundary. This allows the equilibrium requirement which restricts the orientation of the boundaries at a triple point to be satisfied. Large scale simulations of the evolution of representations of grain structures are presented in an accompanying paper.