@INPROCEEDINGS{LeNeRu08, 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 = {http://numod.ins.uni-bonn.de/research/papers/public/LeNeRu08.pdf}, isbn = {978-1-84821-035-6}, }