Numerical boundary control of multi-dimensional hyperbolic equations

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.