Numerical Boundary Control of Multi-Dimensional Hyperbolic Equations
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866912093135962112 |
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| author | Herty, Michael Hinzmann, Kai Müller, Siegfried Thein, Ferdinand |
| author_facet | Herty, Michael Hinzmann, Kai Müller, Siegfried Thein, Ferdinand |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_21890 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Numerical Boundary Control of Multi-Dimensional Hyperbolic Equations Herty, Michael Hinzmann, Kai Müller, Siegfried Thein, Ferdinand Optimization and Control Numerical Analysis 35L50, 35Q93 (Primary), 93D05 (Secondary) 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. |
| title | Numerical Boundary Control of Multi-Dimensional Hyperbolic Equations |
| topic | Optimization and Control Numerical Analysis 35L50, 35Q93 (Primary), 93D05 (Secondary) |
| url | https://arxiv.org/abs/2410.21890 |