  We present a convergence result for the finite volume method applied to a
particular phase field problem suitable for simulation of pure substance
solidification. The model consists of the heat equation and the phase field
equation with a general form of the reaction term which encompasses a variety
of existing models governing dendrite growth and elementary interface tracking
problems. We apply the well known compact embedding techniques in the context
of the finite volume method on admissible unstructured polyhedral meshes. We
develop the necessary interpolation theory and derive an a priori estimate to
obtain boundedness of the key terms. Based on this estimate, we conclude the
convergence of all of the terms in the equation system.
