@book{Serway2014,
  title     = {Physics for Scientists and Engineers with Modern Physics},
  author    = {Raymond A. Serway and John W. Jewett, Jr.},
  year      = 2014,
  location  = {USA},
  publisher = {Cengage Learning},
  isbn      = 9781133954057,
  lccn      = 2012947242
}
@misc{comsol_fem,
  title  = {Finite Element Method (FEM)},
  author = {{COMSOL Multiphysics}},
  year   = 2024,
  url    = {https://www.comsol.com/multiphysics/finite-element-method}
}
@book{lienhard2019heat,
  title     = {A Heat Transfer Textbook},
  author    = {John H. Lienhard IV and John H. Lienhard V},
  year      = 2019,
  publisher = {Courier Dover Publications},
  address   = {Mineola, New York},
  isbn      = {978-0486837352},
  edition   = {5th}
}
@online{simulate2021fem,
  title  = {Finite Element Method Explained in 3 Levels of Difficulty},
  author = {Dr. Simulate},
  year   = 2024,
  url    = {https://www.youtube.com/watch?v=1wSE6iQiScg}
}
@article{Liu2022,
  title     = {Eighty years of the finite element method: Birth, evolution, and future},
  author    = {Liu, Wing Kam and Li, Shaofan and Park, Harold S},
  year      = 2022,
  journal   = {Archives of Computational Methods in Engineering},
  publisher = {Springer},
  volume    = 29,
  number    = 6,
  pages     = {4431--4453},
  doi       = {10.1007/s11831-022-09740-9}
}
@article{Marolf2001,
  title   = {Introduction to general relativity},
  author  = {Marolf, Donald},
  year    = 2001,
  month   = {07},
  journal = {Physics Today},
  volume  = 54,
  number  = 7,
  pages   = {58--58},
  doi     = {10.1063/1.1397399},
  issn    = {0031-9228}
}
@article{Feit1982,
  title   = {Solution of the Schrödinger equation by a spectral method},
  author  = {M.D Feit and J.A Fleck and A Steiger},
  year    = 1982,
  journal = {Journal of Computational Physics},
  volume  = 47,
  number  = 3,
  pages   = {412--433},
  doi     = {10.1016/0021-9991(82)90091-2},
  issn    = {0021-9991}
}
@book{Bergman2011,
  title     = {Fundamentals of heat and mass transfer},
  author    = {Bergman, Theodore L},
  year      = 2011,
  publisher = {John Wiley \& Sons},
  isbn      = {978-1-119-35388-1}
}
@book{Lukaszewicz2016,
  title     = {Navier--stokes equations},
  author    = {Lukaszewicz, Grzegorz and Kalita, Piotr},
  year      = 2016,
  journal   = {Advances in Mechanics and Mathematics},
  publisher = {Springer},
  volume    = 34,
  doi       = {10.1007/978-3-319-27760-8}
}
@article{Barles1998,
  title     = {Option pricing with transaction costs and a nonlinear Black-Scholes equation},
  author    = {Barles, Guy and Soner, Halil Mete},
  year      = 1998,
  journal   = {Finance and Stochastics},
  publisher = {Springer},
  volume    = 2,
  pages     = {369--397},
  doi       = {10.1007/s007800050046}
}
@book{Boresi2002,
  title     = {Advanced mechanics of materials},
  author    = {Boresi, Arthur P and Schmidt, Richard J},
  year      = 2002,
  publisher = {John Wiley \& Sons},
  isbn      = {978-1-119-62876-7}
}
@book{Griffiths2017,
  title     = {Introduction to Electrodynamics},
  author    = {Griffiths, David J.},
  year      = 2017,
  publisher = {Cambridge University Press},
  doi       = {10.1017/9781108333511},
  place     = {Cambridge},
  edition   = 4
}
@software{jax2018github,
  title   = {{JAX}: composable transformations of {P}ython+{N}um{P}y programs},
  author  = {James Bradbury and Roy Frostig and Peter Hawkins and Matthew James Johnson and Chris Leary and Dougal Maclaurin and George Necula and Adam Paszke and Jake Vander{P}las and Skye Wanderman-{M}ilne and Qiao Zhang},
  year    = 2018,
  url     = {http://github.com/jax-ml/jax},
  version = {0.3.13}
}
@misc{fem_getdp,
  title  = {{GetDP} reference manual: the documentation for {GetDP}, a general environment for the treatment of discrete problems},
  author = {P. Dular and C. Geuzaine},
  note   = {\url{http://getdp.info}}
}
@article{fem_agros,
  title     = {FEM based robust design optimization with Agros and {\=A}rtap},
  author    = {Karban, Pavel and P{\'a}nek, David and Orosz, Tam{\'a}s and Petr{\'a}{\v{s}}ov{\'a}, Iveta and Dole{\v{z}}el, Ivo},
  year      = 2021,
  journal   = {Computers \& Mathematics with Applications},
  publisher = {Elsevier},
  volume    = 81,
  pages     = {618--633},
  doi       = {10.1016/j.camwa.2020.02.010}
}
@article{fem_calculix,
  title   = {Calculix crunchix user's manual version 2.12},
  author  = {Dhondt, Guido},
  year    = 2017,
  journal = {Munich, Germany, accessed Sept},
  volume  = 21,
  pages   = 2017,
  url     = {http://www.dhondt.de}
}
@software{fem_elmerfem,
  title   = {{ElmerFEM}},
  author  = {Ruokolainen, Juha and Råback, Peter and Malinen, Mika and Zwinger, Thomas},
  url     = {https://github.com/ElmerCSC/elmerfem},
  license = {GPL-2.0-or-later}
}
@article{fem_freefem,
  title       = {New development in freefem++},
  author      = {F. Hecht},
  year        = 2012,
  journal     = {Journal of Numerical Mathematics},
  volume      = 20,
  number      = {3-4},
  pages       = {251--266},
  doi         = {10.1515/jnum-2012-0013},
  lastchecked = {2024-12-10}
}
@article{fem_goma,
  title        = {GOMA 6.0 - A Full-Newton Finite Element Program for Free and Moving Boundary Problems with Coupled Fluid/ Solid Momentum, Energy, Mass, and Chemical Species Transport: User’s Guide},
  author       = {Schunk, Peter Randall and Rao, Rekha Ranjana and Chen, Ken S. and Labreche, Duane A. and Sun, Amy Cha-Tien and Hopkins, Matthew M. and Moffat, Harry K. and Roach, Robert Allen and Hopkins, Polly L. and Notz, Patrick K. and Roberts, Scott Alan and Sackinger, Philip A. and Subia, Samuel Ramirez and Wilkes, Edward Dean and Baer, Thomas A. and Noble, David R. and Secor, Robert B.},
  year         = 2013,
  month        = 7,
  journal      = {},
  doi          = {10.2172/1089869},
  url          = {https://www.osti.gov/biblio/1089869},
  abstractnote = {Goma 6.0 is a finite element program which excels in analyses of multiphysical processes, particularly those involving the major branches of mechanics (viz. fluid/solid mechanics, energy transport and chemical species transport). Goma is based on a full-Newton-coupled algorithm which allows for simultaneous solution of the governing principles, making the code ideally suited for problems involving closely coupled bulk mechanics and interfacial phenomena. Example applications include, but are not limited to, coating and polymer processing flows, super-alloy processing, welding/soldering, electrochemical processes, and solid-network or solution film drying. This document serves as a user's guide and reference.},
  place        = {United States}
}
@misc{fem_fenicsx,
  title        = {{DOLFINx}: the next generation {FEniCS} problem solving environment},
  author       = {Baratta, Igor A. and Dean, Joseph P. and Dokken, J{\o}rgen S. and Habera, Michal and Hale, Jack S. and Richardson, Chris N. and Rognes, Marie E. and Scroggs, Matthew W. and Sime, Nathan and Wells, Garth N.},
  year         = 2023,
  doi          = {10.5281/zenodo.10447666},
  howpublished = {preprint}
}
@article{fem_dealii,
  title   = {{The deal.II finite element library: Design, features, and insights}},
  author  = {Arndt, Daniel and Bangerth, Wolfgang and Davydov, Denis and Heister, Timo and Heltai, Luca and Kronbichler, Martin and Maier, Matthias and Pelteret, Jean-Paul and Turcksin, Bruno and Wells, David},
  year    = 2021,
  month   = jan,
  journal = {Computers \& Mathematics with Applications},
  volume  = 81,
  pages   = {407--422},
  doi     = {10.1016/j.camwa.2020.02.022}
}
@article{Sullivan2019,
  title     = {{PyVista}: 3D plotting and mesh analysis through a streamlined interface for the Visualization Toolkit ({VTK})},
  author    = {C. Bane Sullivan and Alexander Kaszynski},
  year      = 2019,
  month     = 05,
  journal   = {Journal of Open Source Software},
  publisher = {The Open Journal},
  volume    = 4,
  number    = 37,
  pages     = 1450,
  doi       = {10.21105/joss.01450},
  url       = {https://doi.org/10.21105/joss.01450}
}
@article{Gmsh,
  title   = {Gmsh: A 3-D finite element mesh generator with built-in pre- and post-processing facilities},
  author  = {Geuzaine, Christophe and Remacle, Jean-François},
  year    = 2009,
  journal = {International Journal for Numerical Methods in Engineering},
  volume  = 79,
  number  = 11,
  pages   = {1309--1331},
  doi     = {10.1002/nme.2579}
}
@software{fastfem,
  title  = {FastFEM},
  author = {Sina Atalay and Sacha Escudier and Kentaro Hanson},
  url    = {http://github.com/fastfem/fastfem}
}
@online{semanticVersioning,
  title  = {Semantic Versioning 2.0.0},
  author = {Preston-Werner, Tom},
  url    = {https://semver.org/}
}
@online{hatch,
  title  = {Hatch},
  author = {Python Packaging Authority},
  url    = {https://github.com/pypa/hatch}
}
@online{mkdocs,
  title  = {MkDocs},
  author = {MkDocs},
  url    = {https://www.mkdocs.org}
}
@online{mkdocsmaterial,
  title  = {MkDocs-Material},
  author = {Martin Donath},
  url    = {https://github.com/squidfunk/mkdocs-material}
}
@online{mkdocstrings,
  title  = {MkDocstrings},
  author = {MkDocstrings},
  url    = {https://github.com/mkdocstrings/mkdocstrings}
}
@online{githubactions,
  title  = {GitHub Actions},
  author = {GitHub},
  url    = {https://github.com/features/actions}
}
@online{ruff,
  title  = {Ruff},
  author = {Astral},
  url    = {https://github.com/astral-sh/ruff}
}
@online{precommit,
  title  = {pre-commit},
  author = {pre-commit},
  url    = {https://pre-commit.com}
}
@misc{pytest,
  title  = {PyTest},
  author = {Krekel, Holger and Oliveira, Bruno and Pfannschmidt, Ronny and Bruynooghe, Floris and Laugher, Brianna and Bruhin, Florian},
  year   = {2004},
  url    = {https://github.com/pytest-dev/pytest}
}
@software{black,
  author  = {Langa, Łukasz and {contributors to Black}},
  license = {MIT},
  title   = {{Black: The uncompromising Python code formatter}},
  url     = {https://github.com/psf/black}
}

@article{Patera1984,
title = {A spectral element method for fluid dynamics: Laminar flow in a channel expansion},
journal = {Journal of Computational Physics},
volume = {54},
number = {3},
pages = {468-488},
year = {1984},
issn = {0021-9991},
doi = {https://doi.org/10.1016/0021-9991(84)90128-1},
url = {https://www.sciencedirect.com/science/article/pii/0021999184901281},
author = {Anthony T Patera},
abstract = {A spectral element method that combines the generality of the finite element method with the accuracy of spectral techniques is proposed for the numerical solution of the incompressible Navier-Stokes equations. In the spectral element discretization, the computational domain is broken into a series of elements, and the velocity in each element is represented as a high-order Lagrangian interpolant through Chebyshev collocation points. The hyperbolic piece of the governing equations is then treated with an explicit collocation scheme, while the pressure and viscous contributions are treated implicitly with a projection operator derived from a variational principle. The implementation of the technique is demonstrated on a one-dimensional inflow-outflow advection-diffusion equation, and the method is then applied to laminar two-dimensional (separated) flow in a channel expansion. Comparisons are made with experiment and previous numerical work.}
}

@book{Quarteroni2007,
  title={Numerical Mathematics},
  author={Quarteroni, A. and Sacco, R. and Saleri, F.},
  isbn={9783540346586},
  lccn={99059414},
  series={Texts in Applied Mathematics},
  url={https://books.google.com/books?id=Y7grAAAAYAAJ},
  year={2007},
  publisher={Springer}
}