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.
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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.