DISCRETE CONSERVATION LAWS ON EVOLVING SURFACES

摘要

In this paper we shall introduce a simple effective numerical method for solving diffusion equations on evolving surfaces. Instead of using the finite element method, we shall follow the traditional way to approximate the regular evolving surfaces under consideration by evolving triangular meshes. The key idea of our two-step algorithm is to develop an intrinsic method to compute directly the partial derivatives of functions and indirectly the mean curvatures of the evolving triangular meshes. Most importantly, conservational laws on evolving triangular meshes for diffusion equations are fulfilled.