@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},
}