Consider, the Poisson problem

As trial functions for we use specially tailored wavelets with homogeneous and/or periodic BC. The next section contains more details on such wavelets and how to use them.

Now, the difficult thing is to find a numerical approximation to . This function should be as smooth as possible, as we apply the discrete operator to it for the calculation of the modified right hand side in (5.2). In sections 5.2 and 5.3 it is briefly explained how is determined.

- Homogeneous or periodic boundary conditions
- Dirichlet boundary conditions
- Neumann boundary conditions