In this talk, we discuss discrete conservation laws for diffusion equations over triangular surface meshes. We design a simple, effective numerical method to compute differential operators for scalar and vector-valued functions on surfaces. The key idea of our method is to use the concept of local dual meshes, which are determined by the centroid points of the triangles in the original meshes. The Green formula will provide us a natural way to give a discrete approximation of the Laplace–Beltrami operators on functions over curved regular surfaces. Our discrete Laplace–Beltrami operators have the local property: it only involves the information on the 1-ring of neighboring vertices. Moreover, the discrete conservation laws are fulfilled on the dual meshes for our algorithm.

 

This is joint work with Jyh-Yang Wu(CCU).