  The paper presents the results of numerical solution of the evolution law for
the constrained mean-curvature flow. This law originates in the theory of phase
transitions for crystalline materials and describes the evolution of closed
embedded curves with constant enclosed area. It is reformulated by means of the
direct method into the system of degenerate parabolic partial differential
equations for the curve parametrization. This system is solved numerically and
several computational studies are presented as well.
