High-Order Implicit Time-Marching Methods Based on Generalized Summation-By-Parts Operators

@article{Boom2015HighOrderIT,
  title={High-Order Implicit Time-Marching Methods Based on Generalized Summation-By-Parts Operators},
  author={Pieter D. Boom and David W. Zingg},
  journal={SIAM J. Scientific Computing},
  year={2015},
  volume={37}
}
This article extends the theory of classical finite-difference summation-by-parts (FD-SBP) time-marching methods to the generalized summation-by-parts (GSBP) framework. Dual-consistent GSBP time-marching methods are shown to retain A- and L-stability, as well as superconvergence of integral functionals when integrated with the quadrature associated with the discretization. This also implies that the solution approximated at the end of each time step is superconvergent. In addition, GSBP time… CONTINUE READING

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Extension of Tensor-Product Generalized and Dense-Norm Summation-by-Parts Operators to Curvilinear Coordinates

David C. Del Rey Fernández, Pieter D. Boom, Mark H. Carpenter, David W. Zingg
  • J. Sci. Comput.
  • 2019
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