  In this note we shall introduce a simple, effective numerical method for
solving partial differential equations for scalar and vector-valued data
defined on surfaces. Even though we shall follow the traditional way to
approximate the regular surfaces under consideration by triangular meshes, the
key idea of our algorithm is to develop an intrinsic and unified way to compute
directly the partial derivatives of functions defined on triangular meshes. We
shall present examples in computer graphics and image processing applications.
