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arXiv · 2410.21890

Numerical Boundary Control of Multi-Dimensional Hyperbolic Equations

Michael Herty·Kai Hinzmann·Siegfried Müller·Ferdinand Thein
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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.

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Michael Herty, Kai Hinzmann, Siegfried Müller, Ferdinand Thein. 2024-10-29. Numerical Boundary Control of Multi-Dimensional Hyperbolic Equations. https://arxiv.org/abs/2410.21890

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