A Convergent Finite Volume type O-method on Evolving Surfaces
نویسنده
چکیده
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.
منابع مشابه
A Convergent Finite Volume Scheme for Diffusion on Evolving Surfaces
A finite volume scheme for transport and diffusion problems on evolving hypersurfaces is discussed. 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 simplicial meshes, where grid vertices move on motion trajectories, a consistent...
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