Abstract
The Galerkin method is a very general framework of methods which is very robust. The idea is as follows. Starting from a variational problem set in an infinite dimensional space, a sequence of finite dimensional approximation spaces is defined. The corresponding finite dimensional approximated problems are then solved, which is usually easier to do than trying it straight in infinite dimension. Finally, the dimension of the approximation spaces is left to tend to infinity, and one has to pass to the limit one way or another in the sequence of approximated solutions in order to construct a solution of the original problem.
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