[dune-pdelab] Time derivative of two primary variables in one operator

[Patrick Schmidt]

Good day,


I'm trying to implement the Biot's equation for porous elastic material in Dune PDELab. So far I used the theta method to discretize  in time. At one point I'm struggling with the implementation. Just to give a brief overview of the equation which defines the pressure behaviour you can find it below.


A * dp/dt - B * div(grad(p)) + C*div(du/dt) = 0


where A,B, and C are arbitrary constants. In the case that the fluid is incompressible the first term can be neglected and only the derivative in time for the displacement is taken into account. I split the problem in two local operators like shown in the howto examples. One for the time independent and one for the time dependent terms. In case of incompressible fluids and only one derivative in time that works perfectly for me, but once I try to solve the equation above, where I need to discretize pressure and displacement in time the results are not  fulfilling any longer. Is there any way I have to treat the problem differently?


Cheers,

Patrick
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