In the Poisson equation, when Dirichlet Boundary condition is u=0, I want to solve the problem through the general polygon mesh.
poisson equation
Please see these three questions.

For the situation above, does refining the mesh closer to the boundary reduce the error in the PDE solution?

For the situation above, Which mesh is better, A or B? Could you tell me why?
A: There are the number of elements 4000 in mesh.
B: The number of elements are the same as A, but when it is close to the boundary, it is more refined. And when it is close to the center, it is more coarse. 
If Q2 is correct, does the result would be changed when the Boundary condition was changed?