1. The problem statement, all variables and given/known data I am using the boundary element method to solve unknowns to the Laplace equation from classic potential flow theory for the time evolution of a fluid air interface. At each time step, I need to solve a material derivative equation numerically at every node along an interface to find the new velocity potential. In order to calculate the material derivative, I need to calculate the local interface curvature (et al.). 2. Relevant equations From text, the local (mean) interface curvature can be calculated as 2H=div n. Where H is the mean interface curvature and n is the unit normal to the surface. 3. The attempt at a solution The divergence of a vector field is a somewhat trivial calculation, e.g.: div F = (dF1/dx+dF2/dy+dF3/z) where each value of F is some function that can be differentiated (pde) (like x*y^2). So here is the problem/question, in the case of the unit normal, the values are scalar values (such as [1 0 1]'), therefore if I differentiate each of these values with respect to the independent variable the entire equation equals zero. No doubt I am missing something fundamental here, any advise would be greatly appreciated. I've attached a very simple sketch of a local discretized interface with nodes, and a unit normal just to help visualize what I am working with.