StableSpectralElements.jl is a Julia framework for the numerical solution of hyperbolic and mixed hyperbolic-parabolic conservation laws on general unstructured grids using provably stable discontinuous spectral-element methods with the summation-by-parts property, with an emphasis on dispatched strategies for the evaluation of a broad class of discretization operators.
StableSpectralElements.jl is a registered Julia package (compatible with Julia versions 1.10 and above) and can be installed by entering the following commands within the Julia REPL:
using Pkg; Pkg.add("StableSpectralElements")For further information on the functionality and usage of this package, please refer to the example notebooks as well as the documentation, or feel free to send me an email. If you suspect something is not working properly, or have an idea for how to improve StableSpectralElements.jl, please file an issue. Contributions from the community are always welcome!
If you use StableSpectralElements.jl in your research, please cite the following publications:
@article{MontoyaZinggTensorProduct24,
title = {Efficient Tensor-Product Spectral-Element Operators with the Summation-by-Parts
Property on Curved Triangles and Tetrahedra},
author = {Montoya, Tristan and Zingg, David W},
journal = {{SIAM} Journal on Scientific Computing},
volume = {46},
number = {4},
pages = {A2270--A2297},
doi = {10.1137/23M1573963},
year = {2024}
}
@article{MontoyaZinggEntropyStable24,
title = {Efficient Entropy-Stable Discontinuous Spectral-Element Methods Using
Tensor-Product Summation-by-Parts Operators on Triangles and Tetrahedra},
author = {Montoya, Tristan and Zingg, David W},
journal = {Journal of Computational Physics},
volume = {516},
pages = {113360},
doi = {10.1016/j.jcp.2024.113360},
year = {2024}
}This software is released under the GPLv3 license.