The finite element method (FEM) is one of most important techniques for approximating solutions of elliptic partial differential equations. The lecture course covers the theoretical and algorithmic foundations of the FEM.

The outline of the lecture reads as follows: (1) Introduction: Examples of elliptic PDEs (2) Variational formulation of the elliptic boundary value problems (3) Function spaces and functional analytic framework of the FEM (4) Error analysis and convergence of the P1-FEM in 2D and 3D (5) Algorithmic realization and implementation of FEM (6) saddle point problems and mixed FEM