Numerical Boundary Control of Multi-Dimensional Hyperbolic Equations
Optimization and Control
2024-10-30 v1 Numerical Analysis
Numerical Analysis
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.
Cite
@article{arxiv.2410.21890,
title = {Numerical Boundary Control of Multi-Dimensional Hyperbolic Equations},
author = {Michael Herty and Kai Hinzmann and Siegfried Müller and Ferdinand Thein},
journal= {arXiv preprint arXiv:2410.21890},
year = {2024}
}