Lecture Notes: The Galerkin Method
arXiv:1112.1176h-index: 7
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Educational resource for students learning numerical methods, but no novel research contributions.
These lecture notes introduce the Galerkin method for approximating solutions to PDEs and integral equations, including computational examples and a proof of existence for a nonlinear boundary value problem.
These lecture notes introduce the Galerkin method to approximate solutions to partial differential and integral equations. We begin with some analysis background to introduce this method in a Hilbert Space setting, and subsequently illustrate some computational examples with the help of a sample matlab code. Finally, we use the Galerkin method to prove the existence of solutions of a nonlinear boundary value problem.