@INPROCEEDINGS{Ne10, author = {Nemadjieu, Simplice Firmin}, title = {A Convergent Finite Volume type O-method on Evolving Surfaces}, booktitle = {Proceedings of the 8th International Conference of Numerical Analysis and Applied Mathematics}, year = {2010}, volume = {1281}, series = {AIP Conference Proceedings}, pages = {2184--2187}, abstract = {We present a finite volume scheme for anisotropic diffusion on evolving hypersurfaces. The underlying motion is assumed to be described by a fixed, not necessarily normal, velocity field. The ingredients of the numerical method are an approximation of the family of surfaces by a family of interpolating polygonal meshes, where grid vertices move on motion trajectories, a consistent finite volume discretization of the induced transport on the cells (polygonal patches), and a proper incorporation of a diffusive flux balance at polygonal faces. The main stability results and convergence estimate are obtained.}, doi = {10.1063/1.3498404}, pdf = {http://numod.ins.uni-bonn.de/research/papers/public/Ne10.pdf}, journal = {AIP Conference Proceedings} }