@article{arruda1993largestretch,
  title     = {A three-dimensional constitutive model for the large stretch behavior of rubber elastic materials},
  author    = {Arruda, Ellen M and Boyce, Mary C},
  journal   = {Journal of the Mechanics and Physics of Solids},
  volume    = {41},
  number    = {2},
  pages     = {389--412},
  year      = {1993},
  publisher = {Elsevier},
  doi       = {10.1016/0022-5096(93)90013-6}
}

@book{belytschko2013nonlinear,
  title     = {Nonlinear finite elements for continua and structures},
  author    = {Belytschko, Ted and Liu, Wing Kam and Moran, Brian and Elkhodary, Khalil},
  year      = {2013},
  publisher = {John wiley \& sons}
}

@article{brown2010,
  adsurl  = {https://doi.org/10.1007/s10915-010-9396-8},
  author  = {{Brown}, J.},
  journal = {Journal of Scientific Computing},
  volume  = 45,
  month   = oct,
  title   = {{Efficient Nonlinear Solvers for Nodal High-Order Finite Elements in 3D}},
  year    = 2010,
  doi     = {10.1007/s10915-010-9396-8}
}

@article{giraldoetal2010,
  author  = {Giraldo, F. X. and Restelli, M. and Läuter, M.},
  title   = {Semi-Implicit Formulations of the Navier–Stokes Equations: Application to Nonhydrostatic Atmospheric Modeling},
  journal = {SIAM Journal on Scientific Computing},
  volume  = {32},
  number  = {6},
  pages   = {3394--3425},
  year    = {2010},
  doi     = {10.1137/090775889}
}

@book{holzapfel2000nonlinear,
  author    = {Holzapfel, Gerhard},
  title     = {Nonlinear solid mechanics: a continuum approach for engineering},
  publisher = {Wiley},
  year      = {2000},
  address   = {Chichester New York},
  isbn      = {978-0-471-82319-3}
}

@article{hughesetal2010,
  title   = {Stabilized Methods for Compressible Flows},
  author  = {Hughes, Thomas J R and Scovazzi, Guglielmo and Tezduyar, Tayfun E},
  journal = {Journal of Scientific Computing},
  volume  = {43},
  pages   = {343--368},
  year    = {2010},
  doi     = {10.1007/s10915-008-9233-5}
}

@book{hughes2012finite,
  title     = {The finite element method: linear static and dynamic finite element analysis},
  author    = {Hughes, Thomas JR},
  year      = {2012},
  publisher = {Courier Corporation}
}

@article{libceed-joss-paper,
  author    = {Jed Brown and Ahmad Abdelfattah and Valeria Barra and Natalie Beams and Jean Sylvain Camier and Veselin Dobrev and Yohann Dudouit and Leila Ghaffari and Tzanio Kolev and David Medina and Will Pazner and Thilina Ratnayaka and Jeremy Thompson and Stan Tomov},
  title     = {{libCEED}: Fast algebra for high-order element-based discretizations},
  journal   = {Journal of Open Source Software},
  year      = {2021},
  publisher = {The Open Journal},
  volume    = {6},
  number    = {63},
  pages     = {2945},
  doi       = {10.21105/joss.02945}
}

@article{papanastasiou1992outflow,
  title   = {A new outflow boundary condition},
  author  = {Papanastasiou, TC and Malamataris, N and Ellwood K},
  year    = {1992},
  month   = mar,
  pages   = {587--608},
  volume  = {14},
  journal = {International Journal for Numerical Methods in Fluids},
  doi     = {10.1002/fld.1650140506}
}

@article{straka1993numerical,
  title     = {Numerical solutions of a non-linear density current: A benchmark solution and comparisons},
  author    = {Straka, Jerry M and Wilhelmson, Robert B and Wicker, Louis J and Anderson, John R and Droegemeier, Kelvin K},
  journal   = {International Journal for Numerical Methods in Fluids},
  volume    = {17},
  number    = {1},
  pages     = {1--22},
  year      = {1993},
  publisher = {Wiley Online Library},
  doi       = {10.1002/fld.1650170103}
}

@article{williams2009roofline,
  title     = {Roofline: an insightful visual performance model for multicore architectures},
  author    = {Williams, Samuel and Waterman, Andrew and Patterson, David},
  journal   = {Communications of the ACM},
  volume    = {52},
  number    = {4},
  pages     = {65--76},
  year      = {2009},
  publisher = {ACM New York, NY, USA},
  doi       = {10.1145/1498765.1498785}
}

@article{davydov2020matrix,
  title     = {A matrix-free approach for finite-strain hyperelastic problems using geometric multigrid},
  author    = {Davydov, Denis and Pelteret, Jean-Paul and Arndt, Daniel and Kronbichler, Martin and Steinmann, Paul},
  journal   = {International Journal for Numerical Methods in Engineering},
  volume    = {121},
  number    = {13},
  pages     = {2874--2895},
  year      = {2020},
  publisher = {Wiley Online Library},
  doi       = {10.1002/nme.6336}
}

@article{zhang2011verification,
  title     = {On the Order of Accuracy and Numerical Performance of Two Classes of Finite Volume WENO Schemes},
  author    = {Zhang, Rui and Zhang, Mengping and Shu, Chi-Wang},
  volume    = {9},
  doi       = {10.4208/cicp.291109.080410s},
  number    = {3},
  journal   = {Communications in Computational Physics},
  publisher = {Cambridge University Press},
  year      = {2011},
  pages     = {807--827}
}

@book{bower2010applied,
  title     = {Applied mechanics of solids},
  author    = {Bower, Allan F},
  year      = {2010},
  publisher = {CRC press},
  isbn      = {978-1-4398-0247-2}
}

@article{whiting2003hierarchical,
  title     = {Hierarchical basis for stabilized finite element methods for compressible flows},
  author    = {Whiting, Christian H and Jansen, Kenneth E and Dey, Saikat},
  journal   = {Computer Methods in Applied Mechanics and Engineering},
  volume    = {192},
  number    = {47-48},
  pages     = {5167--5185},
  year      = {2003},
  publisher = {Elsevier},
  doi       = {10.1016/j.cma.2003.07.011}
}

@book{toro2009,
  title     = {Riemann Solvers and Numerical Methods for Fluid Dynamics},
  author    = {Toro, Eleuterio F.},
  year      = {2009},
  publisher = {Springer, Berlin, Heidelberg},
  isbn      = {978-3-540-49834-6}
}

@misc{sodshocktubewiki,
  title        = {Sod shock tube},
  howpublished = {\url{https://en.wikipedia.org/wiki/Sod_shock_tube}},
  note         = {Accessed: 01-30-2022}
}

@article{tezduyar2007yzb,
  title     = {{SUPG} finite element computation of inviscid supersonic flows with $YZ\beta$ shock capturing},
  author    = {Tezduyar, Tayfun E and Senga, Masayoshi},
  journal   = {Computers and Fluids},
  volume    = {36},
  number    = {1},
  pages     = {147-159},
  year      = {2007},
  publisher = {Elsevier},
  doi       = {10.1016/j.compfluid.2005.07.009}
}

@phdthesis{whitingStabilizedFEM1999,
  title   = {Stabilized {{Finite Element Methods}} for {{Fluid Dynamics}} Using a {{Hierarchical Basis}}},
  author  = {Whiting, Christian H},
  year    = {1999},
  address = {{Troy, NY}},
  langid  = {english},
  school  = {Rennselear Polytechnic Institute}
}

@article{shurSTG2014,
  title   = {Synthetic Turbulence Generators for {RANS-LES} Interfaces in Zonal Simulations of Aerodynamic and Aeroacoustic Problems},
  author  = {Shur, Michael L. and Spalart, Philippe R. and Strelets, Michael K. and Travin, Andrey K.},
  year    = {2014},
  journal = {Flow, Turbulence and Combustion},
  volume  = {93},
  number  = {1},
  pages   = {63--92},
  doi     = {10.1007/s10494-014-9534-8},
  langid  = {english}
}

@inproceedings{mengaldoCompressibleBC2014,
  title     = {A Guide to the Implementation of Boundary Conditions in Compact High-Order Methods for Compressible Aerodynamics},
  booktitle = {{{AIAA Aviation}} 2014},
  author    = {Mengaldo, Gianmarco and De Grazia, Daniele and Peiro, Joaquim and Farrington, Antony and Witherden, Freddie and Vincent, Peter and Sherwin, Spencer},
  year      = {2014},
  month     = jun,
  publisher = {{AIAA}},
  address   = {{Atlanta}},
  doi       = {10.2514/6.2014-2923}
}

@article{shakib1991femcfd,
  title     = {A new finite element formulation for computational fluid dynamics: {X}. The compressible {Euler} and {Navier-Stokes} equations},
  author    = {Shakib, Farzin and Hughes, Thomas JR and Johan, Zden{\v{e}}k},
  journal   = {Computer Methods in Applied Mechanics and Engineering},
  volume    = {89},
  number    = {1-3},
  pages     = {141--219},
  year      = {1991},
  publisher = {Elsevier},
  doi       = {10.1016/0045-7825(91)90041-4}
}