668	RWTH Publication No: 996240        2024
TITLE	Numerical Boundary Control of Multi-Dimensional Hyperbolic Equations
AUTHORS	Michael Herty, Kai Hinzmann, Siegfried Müller, Ferdinand Thein
ABSTRACT	Existing theoretical stabilization results for linear, hyperbolic multi-dimensional problems are extended to the discretized multi-dimensional problems. In contrast to existing theoretical and numerical analysis in the spatially one-dimensional case the effect of the numerical dissipation is analyzed and explicitly quantified. Further, using dimensional splitting, the numerical analysis is extended to the multi-dimensional case. The findings are confirmed by numerical simulations for low-order and high-order DG schemes both in the one-dimensional and two-dimensional case.
KEYWORDS	Boundary feedback control, multi-dimensional hyperbolic problem, numerical dissipation, stabilization
CORRESPONDING AUTHOR	Kai Hinzmann