Solver for heat equation with a source term and different boundary conditions #1088
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This part does not make sense: @BilinearForm
def rest(u, v, _):
return dt*h*(u - T_inf)*v It is clearly not bilinear, i.e., linear both in |
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I have never carefully studied time-dependent PDE problems other than learning the basics so I cannot help too much in the implementation or verification. Above I've attempted to use the implicit Euler method which I learned as a student long time ago but haven't used since. It is very simple but I did not verify the result in any way. There must be some test problems available for the heat equation where you can verify that you have implemented the solver correctly, unfortunately I have no time to dig through the references right now. I must say that the package scikit-fem is primarily for the spatial discretization, which I am more familiar with, even though others have demonstrated the application of scikit-fem to the spatial discretization of a time-dependent PDE problem. I'm quite sure many other integrated solvers exist for time-dependent problems that have thoroughly tested physics modules for the heat equation. |
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This part does not make sense:
It is clearly not bilinear, i.e., linear both in$u$ and $v$ .
I suggest you carefully write down the weak formulation of your problem.