Second Order Implicit Schemes for Scalar Conservation Laws

  • Lisa WagnerEmail author
  • Jens Lang
  • Oliver Kolb
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 112)


The today’s demands for simulation and optimization tools for water supply networks are permanently increasing. Practical computations of large water supply networks show that rather small time steps are needed to get sufficiently good approximation results – a typical disadvantage of low order methods. Having this application in mind we use higher order time discretizations to overcome this problem. Such discretizations can be achieved using so-called strong stability preserving Runge-Kutta methods which are especially designed for hyperbolic problems. We aim at approximating entropy solutions and are interested in weak solutions and variational formulations. Therefore our intention is to compare different space discretizations mostly based on variational formulations, and combine them with a second-order two-stage SDIRK method. In this paper, we will report on first numerical results considering scalar hyperbolic conservation laws.


Discontinuous Galerkin Method Total Variation Diminish Water Supply Network Slope Limiter Strong Stability Preserve 
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© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Department of MathematicsDarmstadtGermany
  2. 2.Department of MathematicsThe Darmstadt Graduate Schools of Computational Engineering and Energy Science and EngineeringDarmstadtGermany
  3. 3.Department of MathematicsUniversity of MannheimMannheimGermany

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