Second order derivatives in the PDE Toolbox
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The PDE toolbox is pretty brilliant in that it evaluates the spatial derivitives of your function as well as the function itself in PDE results. Say you have an electric field problem, the PDE toolbox can be used to solve for the electric potential, then combined with evaluateGradient, this can be used to calculate the electric field (See 3:68 in the PDE documentation for a 2D example).
My specific problem used the toolbox for a system of 3 equations in three dimensions. The solution is of the form 3xN_nodes, (ux,uy,uz) leading to gradx being an matrix of the same size with components of the form dux/dx, duy/dx, duz/dx.
It is a useful problem then to find the second order derivatives (d2ux/d2x etc) for a whole host of problems e.g finding the turning points in the electric field.
I wondered then if the PDE toolbox (or any other toolbox which can deal with the results of this form) had any tools similar to evaluateGradient for the second order derivatives. I have searched the documentation but didn't see anything useful.
Any suggestions or direction greatly appreciated. I think perhaps the optimisation toolbox would use these derivatives to find maxima or minima but I wouldn't know where to start (or if different toolboxes can even be interfaced).