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arXiv · 1810.04278

Time discretization schemes for hyperbolic systems on networks by $ε$-expansion

Robert Altmann·Christoph Zimmer
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Abstract

We consider partial differential equations on networks with a small parameter $ε$, which are hyperbolic for $ε>0$ and parabolic for $ε=0$. With a combination of an $ε$-expansion and Runge-Kutta schemes for constrained systems of parabolic type, we derive a new class of time discretization schemes for hyperbolic systems on networks, which are constrained due to interconnection conditions. For the analysis we consider the coupled system equations as partial differential-algebraic equations based on the variational formulation of the problem. We discuss well-posedness of the resulting systems and estimate the error caused by the $ε$-expansion.

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Robert Altmann, Christoph Zimmer. 2019-01-22. Time discretization schemes for hyperbolic systems on networks by $ε$-expansion. https://arxiv.org/abs/1810.04278

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