Time Discretization Schemes for Hyperbolic Systems on Networks by ε-Expansion

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Date
2019-02-12MFO Scientific Program
Research in Pairs 2018Series
Oberwolfach Preprints;2019,03Author
Altmann, Robert
Zimmer, Christoph
Metadata
Show full item recordOWP-2019-03
Abstract
We consider partial differential equations on networks with a small parameter $\epsilon$, which are hyperbolic for $\epsilon>0$ and parabolic for $\epsilon=0$. With a combination of an $\epsilon$-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 $\epsilon$-expansion.