Articles | Volume 6, issue 6
https://doi.org/10.5194/gmd-6-2099-2013
https://doi.org/10.5194/gmd-6-2099-2013
Development and technical paper
 | 
17 Dec 2013
Development and technical paper |  | 17 Dec 2013

Automating the solution of PDEs on the sphere and other manifolds in FEniCS 1.2

M. E. Rognes, D. A. Ham, C. J. Cotter, and A. T. T. McRae

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Cited articles

Alnæs, M. S.: UFL: a finite element form language, in: Automated Solution of Differential Equations by the Finite Element Method, vol. 84 of Lecture Notes in Computational Science and Engineering, edited by: Logg, A., Mardal, K.-A., and Wells, G. N., chap. 17, Springer, 2012.
Alnæs, M. S., Logg, A., Mardal, K.-A., Skavhaug, O., and Langtangen, H. P.: Unified Framework for Finite Element Assembly, Int. J. Computat. Sci. Eng., 4, 231–244, https://doi.org/10.1504/IJCSE.2009.029160, 2009.
Alnæs, M. S., Logg, A., and Mardal, K.-A.: UFC: a finite element code generation interface, in: Automated Solution of Differential Equations by the Finite Element Method, Volume 84 of Lecture Notes in Computational Science and Engineering, edited by: Logg, A., Mardal, K.-A., and Wells, G. N., chap. 16, Springer, 2012.
Alnæs, M. S., Logg, A., Ølgaard, K. B., Rognes, M. E., and Wells, G. N.: Unified Form Language: a domain-specific language for weak formulations of partial differential equations, ACM Trans. Mathe. Softw., available at: http://arxiv.org/abs/1211.4047 (last access: 13 December 2013), 2013.
Arakawa, A. and Hsu, Y.-J. G.: Energy conserving and potential-enstrophy dissipating schemes for the shallow water equations, Mon. Weather Rev., 118, 1960–1969, 1990.