Articles | Volume 6, issue 6
https://doi.org/10.5194/gmd-6-2099-2013
© Author(s) 2013. This work is distributed under
the Creative Commons Attribution 3.0 License.
the Creative Commons Attribution 3.0 License.
https://doi.org/10.5194/gmd-6-2099-2013
© Author(s) 2013. This work is distributed under
the Creative Commons Attribution 3.0 License.
the Creative Commons Attribution 3.0 License.
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
Center for Biomedical Computing, Simula Research Laboratory, P.O. Box 134, 1325 Lysaker, Norway
D. A. Ham
Department of Mathematics, Imperial College London, London SW7 2AZ, UK
Department of Computing, Imperial College London, London SW7 2AZ, UK
C. J. Cotter
Department of Mathematics, Imperial College London, London SW7 2AZ, UK
A. T. T. McRae
Department of Mathematics, Imperial College London, London SW7 2AZ, UK
The Grantham Institute for Climate Change, Imperial College London, London SW7 2AZ, UK
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37 citations as recorded by crossref.
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- Compatible finite element spaces for geophysical fluid dynamics A. Natale et al. https://doi.org/10.1093/climsys/dzw005
- A stabilized reduced integration cell-based smoothed finite element method for incompressible laminar flow C. Jiang et al. https://doi.org/10.1063/5.0264825
- Diffusion MRI simulation in thin-layer and thin-tube media using a discretization on manifolds V. Nguyen et al. https://doi.org/10.1016/j.jmr.2019.01.002
- Automated Generation and Symbolic Manipulation of Tensor Product Finite Elements A. McRae et al. https://doi.org/10.1137/15M1021167
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- A conservative staggered discontinuous Galerkin method on triangular grids for the shallow water equations W. Leng et al. https://doi.org/10.1016/j.jcp.2025.114503
- A comparison of variational upwinding schemes for geophysical fluids, and their application to potential enstrophy conserving discretisations D. Lee et al. https://doi.org/10.1016/j.camwa.2024.04.016
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- 3D mesh processing using GAMer 2 to enable reaction-diffusion simulations in realistic cellular geometries C. Lee et al. https://doi.org/10.1371/journal.pcbi.1007756
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37 citations as recorded by crossref.
- A reduced-dimensional model for near-wall transport in cardiovascular flows K. Hansen & S. Shadden https://doi.org/10.1007/s10237-015-0719-4
- The scaling and skewness of optimally transported meshes on the sphere C. Budd et al. https://doi.org/10.1016/j.jcp.2018.08.028
- Technical note: Finite element formulations to map discrete fracture elements in three-dimensional groundwater models R. de Rooij https://doi.org/10.5194/hess-29-2697-2025
- Boundary-aware hodge decompositions for piecewise constant vector fields K. Poelke & K. Polthier https://doi.org/10.1016/j.cad.2016.05.004
- A Shape Newton Scheme for Deforming Shells with Application to Capillary Bridges S. Schmidt et al. https://doi.org/10.1137/20M1389054
- ConvPDE-UQ: Convolutional neural networks with quantified uncertainty for heterogeneous elliptic partial differential equations on varied domains N. Winovich et al. https://doi.org/10.1016/j.jcp.2019.05.026
- Compatible finite element interpolated neural networks S. Badia et al. https://doi.org/10.1016/j.cma.2025.117889
- Approximations on Convex Star-Type Manifolds I. Burova et al. https://doi.org/10.37394/232018.2026.14.59
- GridapDistributed: a massively parallel finite element toolbox in Julia S. Badia et al. https://doi.org/10.21105/joss.04157
- A mixed mimetic spectral element model of the rotating shallow water equations on the cubed sphere D. Lee & A. Palha https://doi.org/10.1016/j.jcp.2018.08.042
- Firedrake-Fluids v0.1: numerical modelling of shallow water flows using an automated solution framework C. Jacobs & M. Piggott https://doi.org/10.5194/gmd-8-533-2015
- Efficient Numerical Solution of Geometric Inverse Problems Involving Maxwell's Equations Using Shape Derivatives and Automatic Code Generation S. Schmidt et al. https://doi.org/10.1137/16M110602X
- A Numerical Framework for Efficient Motion Estimation on Evolving Sphere-Like Surfaces Based on Brightness and Mass Conservation Laws L. Lang https://doi.org/10.1137/18M1185260
- A quasi-Hamiltonian discretization of the thermal shallow water equations C. Eldred et al. https://doi.org/10.1016/j.jcp.2018.10.038
- Code Generation for Generally Mapped Finite Elements R. Kirby & L. Mitchell https://doi.org/10.1145/3361745
- Bayesian estimations of orientation distribution functions from small-angle scattering enable direct prediction of mechanical stress in anisotropic materials P. Corona et al. https://doi.org/10.1103/PhysRevMaterials.5.065601
- Compatible finite element spaces for geophysical fluid dynamics A. Natale et al. https://doi.org/10.1093/climsys/dzw005
- A stabilized reduced integration cell-based smoothed finite element method for incompressible laminar flow C. Jiang et al. https://doi.org/10.1063/5.0264825
- Diffusion MRI simulation in thin-layer and thin-tube media using a discretization on manifolds V. Nguyen et al. https://doi.org/10.1016/j.jmr.2019.01.002
- Automated Generation and Symbolic Manipulation of Tensor Product Finite Elements A. McRae et al. https://doi.org/10.1137/15M1021167
- Firedrake F. Rathgeber et al. https://doi.org/10.1145/2998441
- A conservative staggered discontinuous Galerkin method on triangular grids for the shallow water equations W. Leng et al. https://doi.org/10.1016/j.jcp.2025.114503
- A comparison of variational upwinding schemes for geophysical fluids, and their application to potential enstrophy conserving discretisations D. Lee et al. https://doi.org/10.1016/j.camwa.2024.04.016
- Total Generalized Variation of the Normal Vector Field and Applications to Mesh Denoising L. Baumgärtner et al. https://doi.org/10.1137/25M1779437
- IRENE: a fluId layeR finitE-elemeNt softwarE D. Wörthmüller et al. https://doi.org/10.1016/j.cpc.2026.110366
- Divergence‐free tangential finite element methods for incompressible flows on surfaces P. Lederer et al. https://doi.org/10.1002/nme.6317
- Fourth-Order Time-Stepping For Stiff PDEs On The Sphere H. Montanelli & Y. Nakatsukasa https://doi.org/10.1137/17M1112728
- Optimal-Transport--Based Mesh Adaptivity on the Plane and Sphere Using Finite Elements A. McRae et al. https://doi.org/10.1137/16M1109515
- Analysis and an Interior-Point Approach for TV Image Reconstruction Problems on Smooth Surfaces M. Herrmann et al. https://doi.org/10.1137/17M1128022
- 3D mesh processing using GAMer 2 to enable reaction-diffusion simulations in realistic cellular geometries C. Lee et al. https://doi.org/10.1371/journal.pcbi.1007756
- Gradient-enhanced damage modeling in Kirchhoff–Love shells: Application to isogeometric analysis of composite laminates M. Pigazzini et al. https://doi.org/10.1016/j.cma.2018.10.042
- Simple and extensible plate and shell finite element models through automatic code generation tools J. Hale et al. https://doi.org/10.1016/j.compstruc.2018.08.001
- Transient structures in rupturing thin films: Marangoni-induced symmetry-breaking pattern formation in viscous fluids L. Shen et al. https://doi.org/10.1126/sciadv.abb0597
- An optimal transport approach for 3D electrical impedance tomography G. Bao & Y. Zhang https://doi.org/10.1088/1361-6420/ad89f3
- Hierarchical high order finite element bases for H(div) spaces based on curved meshes for two-dimensional regions or manifolds D. Castro et al. https://doi.org/10.1016/j.cam.2016.01.053
- Abstractions and Automated Algorithms for Mixed Domain Finite Element Methods C. Daversin-Catty et al. https://doi.org/10.1145/3471138
- A versatile FEM framework with native GPU scalability via globally-applied AD M. Pundir et al. https://doi.org/10.1016/j.cma.2026.119118
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