# In the method of weighted residual, is it necessary for the basis function to satisfy the boundary conditions?

In the method of weighted residual applied to boundary value problems, is it necessary for the basis function to satisfy all of the boundary conditions? Will it work even if it does not satisfy all of the boundary conditions?

The test functions must come from the space of variations, i.e., if your solution has to satisfy $$u|_{\partial \Omega}=g$$ then your test functions have to satisfy $$v|_{\partial \Omega}=0.$$
• Could you please explain a bit more on the 'space of variations'? If $u|_{\partial \Omega}=0$, can $v|_{\partial \Omega}\neq0$? Apr 2 '15 at 13:25