Welcome to libCEED’s User Manual!


Indices and tables


Sod shock tube. https://en.wikipedia.org/wiki/Sod_shock_tube. Accessed: 01-30-2022.


Ellen M Arruda and Mary C Boyce. A three-dimensional constitutive model for the large stretch behavior of rubber elastic materials. Journal of the Mechanics and Physics of Solids, 41(2):389–412, 1993. doi:10.1016/0022-5096(93)90013-6.


Jed Brown, Ahmad Abdelfattah, Valeria Barra, Natalie Beams, Jean Sylvain Camier, Veselin Dobrev, Yohann Dudouit, Leila Ghaffari, Tzanio Kolev, David Medina, Will Pazner, Thilina Ratnayaka, Jeremy Thompson, and Stan Tomov. libCEED: fast algebra for high-order element-based discretizations. Journal of Open Source Software, 6(63):2945, 2021. doi:10.21105/joss.02945.


Denis Davydov, Jean-Paul Pelteret, Daniel Arndt, Martin Kronbichler, and Paul Steinmann. A matrix-free approach for finite-strain hyperelastic problems using geometric multigrid. International Journal for Numerical Methods in Engineering, 121(13):2874–2895, 2020. doi:10.1002/nme.6336.


F. X. Giraldo, M. Restelli, and M. Läuter. Semi-implicit formulations of the navier–stokes equations: application to nonhydrostatic atmospheric modeling. SIAM Journal on Scientific Computing, 32(6):3394–3425, 2010. doi:10.1137/090775889.


Gerhard Holzapfel. Nonlinear solid mechanics: a continuum approach for engineering. Wiley, Chichester New York, 2000. ISBN 978-0-471-82319-3.


Thomas J R Hughes, Guglielmo Scovazzi, and Tayfun E Tezduyar. Stabilized methods for compressible flows. Journal of Scientific Computing, 43:343–368, 2010. doi:10.1007/s10915-008-9233-5.


Thomas JR Hughes. The finite element method: linear static and dynamic finite element analysis. Courier Corporation, 2012.


TC Papanastasiou, N Malamataris, and Ellwood K. A new outflow boundary condition. International Journal for Numerical Methods in Fluids, 14:587–608, March 1992. doi:10.1002/fld.1650140506.


Jerry M Straka, Robert B Wilhelmson, Louis J Wicker, John R Anderson, and Kelvin K Droegemeier. Numerical solutions of a non-linear density current: a benchmark solution and comparisons. International Journal for Numerical Methods in Fluids, 17(1):1–22, 1993. doi:10.1002/fld.1650170103.


Tayfun E Tezduyar and Masayoshi Senga. SUPG finite element computation of inviscid supersonic flows with $yz\beta $ shock capturing. Computers and Fluids, 36(1):147–159, 2007. doi:10.1016/j.compfluid.2005.07.009.


Eleuterio F. Toro. Riemann Solvers and Numerical Methods for Fluid Dynamics. Springer, Berlin, Heidelberg, 2009. ISBN 978-3-540-49834-6.


Christian H Whiting. Stabilized Finite Element Methods for Fluid Dynamics Using a Hierarchical Basis. PhD thesis, Rennselear Polytechnic Institute, Troy, NY, 1999.


Christian H Whiting, Kenneth E Jansen, and Saikat Dey. Hierarchical basis for stabilized finite element methods for compressible flows. Computer Methods in Applied Mechanics and Engineering, 192(47-48):5167–5185, 2003. doi:10.1016/j.cma.2003.07.011.


Samuel Williams, Andrew Waterman, and David Patterson. Roofline: an insightful visual performance model for multicore architectures. Communications of the ACM, 52(4):65–76, 2009. doi:10.1145/1498765.1498785.


Rui Zhang, Mengping Zhang, and Chi-Wang Shu. On the order of accuracy and numerical performance of two classes of finite volume weno schemes. Communications in Computational Physics, 9(3):807–827, 2011. doi:10.4208/cicp.291109.080410s.


J. Brown. Efficient Nonlinear Solvers for Nodal High-Order Finite Elements in 3D. Journal of Scientific Computing, October 2010. doi:10.1007/s10915-010-9396-8.