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Hi,

I have a 2D geometry and time-dependent study with 1D heat transfer in solids, 2D chemical reaction and 2D gas diffusion physics, where I'm using the coefficient form PDEs to model the chemical reaction and gas diffusion.

Now I want to rebuild the model but with using the weak form physics for the gas diffusion. My question is how can convert the following equation into the weak form?

dP/dt+∇. (-D ∇P)=f

where :

P is the dependent variable to solve for.

t is time

∇ is [d/dx, d/dy]

f is a function of the gradient of another dependent variable with time (let's call the other variable CA)

I tried the following two formats but the study didn't converge all the way due to either initial values problems or other errors that I didn't get when solving with Coefficient form PDE, which suggests the weak form expression is wrong.

1st trial:

(-d(P, TIME)-d(-D*d(P, x), x)-d(-D*d(P, y), y)+-d(CA, TIME))*test(P)

2nd trial:

-d(P, TIME)*test(P)+D*(Px*test(Px)+Py*test(Py))+ -d(CA, TIME)*test(P)

I know this is rather a "mathematical" question than a technical one, but would appreciate your help. Thanks!

Eman