tensor-product-stokes.bib

@article{canuto1984combined,
  title={Combined finite element and spectral approximation of the {Navier-Stokes} equations},
  author={Canuto, Claudio and Maday, Yvon and Quarteroni, Alfio},
  journal={Numerische Mathematik},
  volume={44},
  number={2},
  pages={201--217},
  year={1984},
  publisher={Springer}
}


@article{jensen1990divergence,
  title={Divergence stability in connection with the p-version of the finite element method},
  author={Jensen, S and Vogelius, M},
  journal={ESAIM: Mathematical Modelling and Numerical Analysis},
  volume={24},
  number={6},
  pages={737--764},
  year={1990},
  publisher={EDP Sciences}
}


@inproceedings{nakahashi1989finite,
  title={A finite-element method on prismatic elements for the three-dimensional {Navier-Stokes} equations},
  author={Nakahashi, Kazuhiro},
  booktitle={11th International Conference on Numerical Methods in Fluid Dynamics},
  pages={434--438},
  year={1989},
  organization={Springer}
}


@article{mcrae2016automated,
  title={Automated generation and symbolic manipulation of tensor product finite elements},
  author={McRae, Andrew TT and Bercea, G-T and Mitchell, Lawrence and Ham, David A and Cotter, Colin J},
  journal={SIAM Journal on Scientific Computing},
  volume={38},
  number={5},
  pages={S25--S47},
  year={2016},
  publisher={SIAM}
}


@article{pechstein2012anisotropic,
  title={Anisotropic mixed finite elements for elasticity},
  author={Pechstein, Astrid and Sch{\"o}berl, Joachim},
  journal={International journal for numerical methods in engineering},
  volume={90},
  number={2},
  pages={196--217},
  year={2012},
  publisher={Wiley Online Library}
}


@book{boffi2013mixed,
  title={Mixed finite element methods and applications},
  author={Boffi, Daniele and Brezzi, Franco and Fortin, Michel and others},
  volume={44},
  year={2013},
  publisher={Springer}
}


@article{cockburn2007note,
  title={A note on discontinuous {Galerkin} divergence-free solutions of the {Navier--Stokes} equations},
  author={Cockburn, Bernardo and Kanschat, Guido and Sch{\"o}tzau, Dominik},
  journal={Journal of Scientific Computing},
  volume={31},
  pages={61--73},
  year={2007},
  publisher={Springer}
}


@manual{FiredrakeUserManual,
  title        = {Firedrake User Manual},
  author       = {David A. Ham and Paul H. J. Kelly and Lawrence Mitchell and Colin J. Cotter and Robert C. Kirby and Koki Sagiyama and Nacime Bouziani and Sophia Vorderwuelbecke and Thomas J. Gregory and Jack Betteridge and Daniel R. Shapero and Reuben W. Nixon-Hill and Connor J. Ward and Patrick E. Farrell and Pablo D. Brubeck and India Marsden and Thomas H. Gibson and Miklós Homolya and Tianjiao Sun and Andrew T. T. McRae and Fabio Luporini and Alastair Gregory and Michael Lange and Simon W. Funke and Florian Rathgeber and Gheorghe-Teodor Bercea and Graham R. Markall},
  organization = {Imperial College London and University of Oxford and Baylor University and University of Washington},
  edition      = {1st},
  year         = {2023},
  month        = {May},
  doi          = {10.25561/104839},
}


@incollection{rognes2012automated,
  title={Automated testing of saddle point stability conditions},
  author={Rognes, Marie E},
  booktitle={Automated Solution of Differential Equations by the Finite Element Method: The FEniCS Book},
  pages={657--671},
  year={2012},
  publisher={Springer}
}


@article{malkus1981eigenproblems,
  title={Eigenproblems associated with the discrete {LBB} condition for incompressible finite elements},
  author={Malkus, DS},
  journal={International Journal of Engineering Science},
  volume={19},
  number={10},
  pages={1299--1310},
  year={1981},
  publisher={Elsevier}
}


@article{hernandez2005slepc,
  title={{SLEPc: A scalable and flexible toolkit for the solution of eigenvalue problems}},
  author={Hernandez, Vicente and Roman, Jose E and Vidal, Vicente},
  journal={ACM Transactions on Mathematical Software (TOMS)},
  volume={31},
  number={3},
  pages={351--362},
  year={2005},
  publisher={ACM New York, NY, USA}
}


@article{isaac2015solution,
  title={Solution of nonlinear {Stokes} equations discretized by high-order finite elements on nonconforming and anisotropic meshes, with application to ice sheet dynamics},
  author={Isaac, Tobin and Stadler, Georg and Ghattas, Omar},
  journal={SIAM Journal on Scientific Computing},
  volume={37},
  number={6},
  pages={B804--B833},
  year={2015},
  publisher={SIAM}
}