Numerical boundary control of multi-dimensional hyperbolic equations

Mathematical Control and Related Fields, vol. 18, pp. 175–200

Abstract

Existing 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.

Authors 4

1. Michaël Herty Aachen Institut für Geometrie und Praktische Mathematik

   University of Pretoria · RWTH Aachen University

   Affiliation as printed

   Extraordinary Professor , Department of Mathematics and Applied Mathematics , University of Pretoria , Private Bag X20 , Hatfield 0028 , South Africa

   Institut für Geometrie und Praktische Mathematik , RWTH Aachen , Templergraben 55 , Aachen , D-52056 , Germany

2. Kai Hinzmann Aachen Institut für Geometrie und Praktische Mathematik

   RWTH Aachen University

   Affiliation as printed

   Institut für Geometrie und Praktische Mathematik, RWTH Aachen, Templergraben 55, Aachen, D-52056, Germany

3. Siegfried Müller Aachen Institut für Geometrie und Praktische Mathematik

   RWTH Aachen University

   Affiliation as printed

   Institut für Geometrie und Praktische Mathematik, RWTH Aachen, Templergraben 55, Aachen, D-52056, Germany

4. Ferdinand Thein corresponding

   Johannes Gutenberg University Mainz

   Affiliation as printed

   Johannes Gutenberg-Universität Mainz, Staudingerweg 9, 55128 Mainz, Germany