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Vietnam Journal of Mathematics

, Volume 46, Issue 4, pp 779–801 | Cite as

Model and Discretization Error Adaptivity Within Stationary Gas Transport Optimization

  • Volker MehrmannEmail author
  • Martin Schmidt
  • Jeroen J. Stolwijk
Article

Abstract

The minimization of operation costs for natural gas transport networks is studied. Based on a recently developed model hierarchy ranging from detailed models of instationary partial differential equations with temperature dependence to highly simplified algebraic equations, modeling and discretization error estimates are presented to control the overall error in an optimization method for stationary and isothermal gas flows. The error control is realized by switching to more detailed models or finer discretizations if necessary to guarantee that a prescribed model and discretization error tolerance is satisfied in the end. We prove convergence of the adaptively controlled optimization method and illustrate the new approach with numerical examples.

Keywords

Gas transport optimization Isothermal stationary Euler equations Model hierarchy Adaptive error control Marking strategy 

Mathematics Subject Classification (2010)

35Q31 65G99 65L70 90C30 93C40 

Notes

Acknowledgements

This research has been performed as part of the Energie Campus Nürnberg and is supported by funding of the Bavarian State Government. The authors acknowledge funding through the DFG Transregio TRR 154, subprojects A05, B03, and B08.

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Copyright information

© Vietnam Academy of Science and Technology (VAST) and Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  1. 1.Institut für MathematikBerlinGermany
  2. 2.Friedrich-Alexander-Universität Erlangen-Nürnberg, Discrete OptimizationErlangenGermany
  3. 3.Energie Campus NürnbergNürnbergGermany

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