This lesson starts with strong and weak forms of 1D linear elliptic PDEs. It is explained what approximations for the strong and weak forms will do. The finite element method is based on the approximation of weak form and the same is expressed here. Instead of infinite functional spaces, the approximations are made in finite-dimensional spaces. The finite-dimensional weak form, or the Galerkin weak form, is written.
In this video we will answer the following question:
For the finite-dimensional weak form, does the equivalence of the strong and the weak form of the PDE still hold?