The course will present an overview of recent developments, which will enable students to make informed choices in terms of discretization and model selection in solving numerical problems in mechanics. We will cover discretization strategies ranging from the standard finite element method, the smoothed finite element method, the extended finite element method, polygonal and virtual element methods, meshfree methods. The applications range between fracture of heterogeneous materials and biomedical simulations.

The intended learning outcomes of the course are such that the students will be:

  • able to critically assess discretization schemes in mechanics
  • able to implement simple error estimators for finite element methods
  • familiar with basic multi-scale methods for fracture and their limitations
  • able to follow basic literature in model error and model selection, in particular based on Bayesian inference

Course participants will learn these topics through lectures and hands-on numerical experiments.