Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars

Speaker:	Dr. Jonas Kohler, Karlsruhe Institute of Technology
Inviter:
Title:	Error analysis of an ADI splitting for discontinuous Galerkin discretizations of linear wave-type problems
Time & Venue:	2019.09.13 10:50-11:35 N204
Abstract:	We consider an alternating direction implicit (ADI) scheme for the time integration of a class of linear wave-type problems of the form on product domains. This class is characterized by the fact that one can split so that the flows of A and B essentially decouple into one-dimensional flows. Important examples for such problems are the 2D advection and wave equations as well as the 3D Maxwell’s equations. Full discretization of (1) is achieved by discretizing the split operators A and B via a central fluxes discontinuous Galerkin scheme and then using the Peaceman–Rachford (PR) scheme for time integration. The aforementioned properties of the split operators A and B then allow for optimal (linear) complexity of the fully discrete scheme, despite it being unconditionally stable. In this talk, we derive error bounds for the full discretization that are of optimal order in time and space and that do not deteriorate under mesh refinement. This is achieved by interpreting the PR scheme as a perturbation of the Crank–Nicolson scheme, enabling us to employ techniques from. However, additional terms arising from the splitting nature of the PR scheme have to be dealt with.