[1] S. F. Nemadjieu. A convergent finite volume type o-method on evolving surfaces. In Proceedings of the 8th International Conference of Numerical Analysis and Applied Mathematics, volume 1281 of AIP Conference Proceedings, pages 2184-2187, 2010.
bib | DOI | .pdf 1 ]
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.