Problem with pdsolve/numeric
I created a routine for solving a thermo-mechanical problem. The size of the spatial domain is a function of time and the thermo-mechanical behavior of the structure.
The solution is obtained by discretizing the time domain in n intervals. The thermo-mechanical responses are obtained at each time t[i] =t[i-1]+dt.
The material exhibits elastic and elastoplastic mechanical behavior and thus the problem was divided into two consecutive phases (phase 1 and 2).
The heat problem is nonlinear because the thermal properties are variable (termal conductivity, specific heat, and density).
In phase 2, the pdsolve/numeric command returns an error for the solution of the heat conduction equation (equation called pde1). I believe this error is related to the derivative of thermal conductivity k(x1) (piecewise function).
I tested many alternatives (I wrote the pde1 equation in two different ways), I checked the routine many times and I don't understand the reason for the error. With each attempt, the command returns a different error.
Thanks for your attention and help.