10.04.14 16:00

Generalized Finite Element Methods: Basic Theory and Applications

Marc Alexander Schweitzer (Bonn)

Generalized Finite Element Methods (GFEM) are modern numerical approaches to the approximation of partial differential equations. A key ingredient in these techniques is the use of problem-dependent basis functions which may even lead to approximation schemes that converge exponentially even for irregular / singular solutions. Another ingredient in GFEM is the use of a partition of unity (PU) to splice the employed problem-depenent local approximation spaces into a global approximation space. For a particular class of PUs, the construction of efficient multilevel solvers and preconditioners as well as lumping strategies are moreover available. We present the fundamental construction principles of GFEM, the basic approximation results as well as details on their efficient parallel implementation. We discuss the properties of GFEM via applications from fracture mechanics, heterogeneous materials and elastic waves.

Kategorie: Kolloquium