author = {Lenz, Martin and Nemadjieu, Simplice Firmin and Rumpf, Martin},
  title = {Finite Volume Method on Moving Surfaces},
  booktitle = {Finite Volumes for Complex Applications V},
  year = {2008},
  editor = {Eymard, Robert and H{\'{e}}rald, Jean-Marc},
  pages = {561--576},
  publisher = {Wiley},
  abstract = {In this paper an evolving surface finite volume method is introduced
	for the numerical resolution of a transport diffusion problem on
	a family of moving hypersurfaces. These surfaces are assumed to evolve
	according to a given motion field. The ingredients of the method
	are an approximation of the family of surfaces by a family of interpolating
	simplicial meshes, where grid vertices move on motion trajectories,
	a consistent finite volume discretization of the induced transport
	on the simplices, and a proper incorporation of a diffusive flux
	balance at simplicial faces. Existence, uniqueness and a priori estimates
	are proved for the discrete solution. Furthermore, a convergence
	result is formulated together a sketch of the proof. Finally, first
	numerical results are discussed.},
  pdf = { 1},
  isbn = {978-1-84821-035-6}