Higher order eXtended discretization methods
Björn Müller (TU Darmstadt, Germany)
Florian Kummer (TU Darmstadt, Germany)
Within the past decade, two important aspects of numerical discretization
schemes have been enhanced with great success. On the one hand, eXtended
discretization methods (XDMS) had a huge impact on the community and are
now readily applicable to industrial scale applications. On the other hand,
discretization schemes that are able to realize higher order convergence rates
on very general domains have attracted great interest. Their main appeal
is due to the fact that they are able to deliver more accurate solutions for
smooth problems using the same number of degrees of freedom as low-order
methods.
A next natural step is the combination of the new developments in both
elds in order to extend the applicability of higher order methods to suitable
non-smooth problems. First promising results have been presented, for example,
using the eXtended Finite Element Method (XFEM), the Finite Cell
Method (FCM) and the Discontunous Galerkin Method (DGM) in the context
of problems with sharp immersed interfaces. However, some challenges
like interface representation, numerical integration and matrix-conditioning
still remain to be solved. The aim of this Minisymposium is thus to bring
together researchers whose contributions help to improve the efficiency and
to extend the applicability of higher order XDMS.
Solution of a Poisson equation with a jump using a second order extended Discontinuous Galerkin discretization (by courtesy of Florian Kummer)
