### Different boundary conditions for the test and trial spaces in 2d

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Consider a general 2d problem (1d space + 1d time). We have homogeneous Dirichlet boundary conditions in space and an initial condition is defined in time. So, the trial (W) and test (V) spaces would be different. The trial functions will be zero at time t=0 and test functions will be zero at t=T (end time). How would one implement this, without manually tinkering the assembled matrix (very bad idea) ?

I did find something relevant from an earlier post:

https://fenicsproject.org/qa/5248/different-boundary-conditions-for-trial-test-function-space/

But it is only in 1d, so I don't know if it will work as it is.

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