Numerical Boundary Control of Multi-Dimensional Hyperbolic Equations

arXiv (Cornell University)

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.

Authors 4

1. Michaël Herty Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen

2. Kai Hinzmann Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen

3. Siegfried Müller Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen

4. Ferdinand Thein