Mathematics

This an advanced monographic course on the numerical analysis of finite element techniques. Each year, the state-of-the-art of a research level topic is selected and presented with strong interaction with the students. This year the course will be devoted to nonconcofming FEM, with particular focus on discontinuous Galerkin methods. Tentative syllabus: - Discontinuous Galerkin (dG) FEM: introduction and motivation - dG time-stepping - dG for steady transport problems - Numerical fluxes - dG for elliptic problems - A priori error analysis - A posteriori error analysis - dG for fluid problems - Extensions to polygonal/polyhedral meshes - Nonconforming methods for forth-order problems