GitHub

Applications

Here is a (non-exhaustive) list of research using SummationByPartsOperators.jl.

  • Jesse Chan, Hendrik Ranocha, Andrés M. Rueda-Ramírez, Gregor Gassner, Tim Warburton (2022). On the Entropy Projection and the Robustness of High Order Entropy Stable Discontinuous Galerkin Schemes for Under-Resolved Flows. arXiv: 2203.10238 [math.NA] DOI: 10.3389/fphy.2022.898028 A reproducibility repository containing source code for all numerical experiments is available at DOI: 10.5281/zenodo.6364108
  • Hendrik Ranocha, Manuel Quezada de Luna, and David I Ketcheson (2021). On the Rate of Error Growth in Time for Numerical Solutions of Nonlinear Dispersive Wave Equations. arXiv: 2102.07376 [math.NA] DOI: 10.1007/s42985-021-00126-3 A reproducibility repository containing source code for all numerical experiments is available at DOI: 10.5281/zenodo.4540467
  • Hendrik Ranocha, Dimitrios Mitsotakis, and David I Ketcheson (2021). A Broad Class of Conservative Numerical Methods for Dispersive Wave Equations. DOI: 10.4208/cicp.OA-2020-0119 A reproducibility repository containing source code for all numerical experiments is available at DOI: 10.5281/zenodo.3908803
  • Philippe G LeFloch and Hendrik Ranocha (2021). Kinetic functions for nonclassical shocks, entropy stability, and discrete summation by parts. DOI: 10.1007/s10915-021-01463-6
  • Jan Nordström and Hendrik Ranocha (2021). A New Class of A Stable Summation by Parts Time Integration Schemes with Strong Initial Conditions. DOI: 10.1007/s10915-021-01454-7 A reproducibility repository containing source code for all numerical experiments is available at DOI: 10.5281/zenodo.3699173
  • Hendrik Ranocha (2021). On Strong Stability of Explicit Runge-Kutta Methods for Nonlinear Semibounded Operators. DOI: 10.1093/imanum/drz070
  • Hendrik Ranocha and David I Ketcheson (2020). Energy Stability of Explicit Runge-Kutta Methods for Nonautonomous or Nonlinear Problems. DOI: 10.1137/19M1290346 A reproducibility repository containing source code for all numerical experiments is available at DOI: 10.5281/zenodo.3464243
  • Hendrik Ranocha, Katharina Ostaszewski, and Philip Heinisch (2020). Discrete Vector Calculus and Helmholtz Hodge Decomposition for Classical Finite Difference Summation by Parts Operators. DOI: 10.1007/s42967-019-00057-2 A reproducibility repository containing source code for all numerical experiments is available at DOI: 10.5281/zenodo.3375170
  • Hendrik Ranocha and Gregor J Gassner (2020). Preventing pressure oscillations does not fix local linear stability issues of entropy-based split-form high-order schemes. arXiv: 2009.13139 [math.NA] A reproducibility repository containing source code for all numerical experiments is available at DOI: 10.5281/zenodo.4054366
  • Philipp Öffner and Hendrik Ranocha (2019). Error Boundedness of Discontinuous Galerkin Methods with Variable Coefficients. DOI: 10.1007/s10915-018-00902-1

If you use this package for your own research, please cite it as described in the documentation and make a PR to add your work to the list above.