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I am considering a coupled PDE system which involves the variables , I want to investigate the behaviour of the third order derivatives of these variables.

As such I want to add a physics which involves the variables:

I then would compute the second order derivatives of these variables and continue on. However, I cannot seem to be able to find a way to do it which does not create errors.

The best approach that I have found is to write a coefficent form PDE, with Dirichlet boundary conditions. The coefficents of all of the constants of the PDE are identically zero except for the absorption coefficent (which is an identity matrix) and the source term.

I then compute the error between my variables and etc. But I find that the error is of the order , when I should expect it to be identically zero.

I have tried all approaches that I can think of: * Applying a pointwise constraint failed to get the process even going. * Creating a second study which just computes Q (not dxQ1 etc.) and then use that as the initial condition for the main study. * Create a variable which would make dxQ1 etc. be identically equal to zero and do an auxhillary study. * Use a general PDE form with a zero flux condition. * Chaning the termination criterion to solution only, and then to residual only.

None of these approaches worked and I have no idea why. My goal is to get the error between dxQ1 and Q1x, dyQ1 and Q1y, dxQ2 and Q2x, and dyQ2 and Q2y, to be zero (or close to). I have attached my code.