When does the finite element method (not) converge?

Václav Kučera (KNM MFF UK, web)
Pondělí 22. května 2017, 14:30 hodin
Místnost G4-MAT, 4. patro budovy G, kampus Husova (Univerzitní nám. 1410/1)

Detailed FEM mesh of steel (Ferenc Nasztanovics)

[Pozvánka v PDF]


The finite element method (FEM) is currently perhaps the most popular method for the numerical solution of partial differential equations. We possess a deep understanding of the theoretical properties of the method, however there are still very basic open questions about the FEM. For example, the question of mesh properties guaranteeing convergence of the method is wide open — we know several sufficient conditions, but not a single necessary condition for convergence.

In this talk we give an overview of the current knowledge and ongoing attempts to formulate a necessary and sufficient condition on mesh geometry guaranteeing FEM convergence. These questions lead to interesting problems about the geometry of the triangle and its partitions.