Abstract:
The aim of this series of lectures is to introduce the audience to the numerical solution of PDEs with finite element techniques.
We will consider both stationary and time-dependent problems. The basic theoretical results will be briefly recalled. Then, the fundamentals of finite element methods will be presented, together with the related convergence properties.
The FreeFem++ package will be used to implement these methods under several circumstances. FreeFem++ is a partial differential equation solver by F. Hecht and collaborators. It has its own language. The scripts can solve linear and nonlinear problems in 2D and 3D.
In particular, we will see how meshes can be constructed, how linear and nonlinear PDEs can be (re)formulated in a weak sense, appropriate for numerical approximation, how large systems of linear algebraic equations can be solved, how solutions can be visualized, etc.