Discrete Conservation Laws on Curved Surfaces

In this paper we shall introduce a simple, effective numerical method to compute differential operators for scalar and vector-valued functions on regular surfaces. The key idea of our algorithm is to develop an intrinsic and unified way to compute directly partial derivatives of functions defined on triangular meshes which are the discretizations of regular surfaces under consideration. Most importantly, the divergence theorem and conservation laws for diffusion equations on triangular meshes are fulfilled.