Numerical boundary control of multi-dimensional hyperbolic equations

dc.contributor.authorHerty, Michael
dc.contributor.authorHinzmann, Kai
dc.contributor.authorMuller, Siegfried
dc.contributor.authorThein, Ferdinand
dc.date.accessioned2026-02-18T12:55:38Z
dc.date.available2026-02-18T12:55:38Z
dc.date.issued2025
dc.description.abstractExisting theoretical stabilization results for linear, hyperbolic multi–dimensional problems are extended to 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.
dc.description.departmentMathematics and Applied Mathematics
dc.description.librarianam2026
dc.description.sdgSDG-04: Quality education
dc.description.sponsorshipFunded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) through SPP 2410 Hyperbolic Balance Laws in Fluid Mechanics: Complexity, Scales, Randomness (CoScaRa) within the Projects 525842 915, 525842915 (Numerical Schemes for Coupled Multi-Scale Problems) and 525939 417 (A Sharp Interface Limit by Vanishing Volume Fraction for Non-Equilibrium Two Phase Flows modeled by Hyperbolic Systems of Balance Laws), through GRK 2379 (IRTG Hierarchical and Hybrid Approaches in Modern Inverse Problems), and through SPP 2183 Eigenschaftsgeregelte Umformprozesse with the Projects 424334423 Entwicklung eines flexiblen isothermen Reckschmiedeprozesses fur die eigenschaftsgeregelte Herstellung von Turbinenschaufeln aus Hochtemperaturwerkstoffen.
dc.description.urihttps://www.aimsciences.org/mcrf
dc.identifier.citationHerty, M., Hinzmann, K., Muller, S. et al. 2025, 'Numerical boundary control of multi-dimensional hyperbolic equations', Mathematical Control and Related Fields, pp. 1-26. DOI:10.3934/mcrf.2025056.
dc.identifier.issn2156-8472 (print)
dc.identifier.issn2156-8499 (online)
dc.identifier.other10.3934/mcrf.2025056
dc.identifier.urihttp://hdl.handle.net/2263/108400
dc.language.isoen
dc.publisherAmerican Institute of Mathematical Sciences
dc.rights© 2025 The Author(s). This is an open access article distributed under the terms of the Creative Commons Attribution-Non Commercial-No Derivatives License 4.0 (CCBY-NC-ND).
dc.subjectBoundary feedback control
dc.subjectMulti-dimensional hyperbolic problem
dc.subjectNumerical dissipation
dc.subjectStabilization
dc.titleNumerical boundary control of multi-dimensional hyperbolic equations
dc.typeArticle

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