Dear all,

Sorry for the spam - a basic mathematical question.

In the step-3 example 
(https://www.dealii.org/8.4.1/doxygen/deal.II/step_3.html), I noticed that 
at first the variable phi is used as a test function. It is in the same 
space with u, except for that the value is 0 on the boundaries. (in this 
problem the boundary values for u is also 0, but it could be non-zero for 
general cases)

However, later, the variable phi is also the shape function. I am lost in 
this step in understanding why the test function could be the shape 
function at the same time. For example, if the boundary conditions of u is 
non-zero, we'd have to have a shape function to be non-zero at the boundary 
(right?) but the test function space needs to be 0 on the boundary.

Could you please help?

Thank you,
Shawn

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