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.
Kdy: pondělí 22. května 2017, 14:30
Kdo: Václav Kučera, MFF UK