Algorithm 839: FIAT, a new paradigm for computing finite element basis functions. Much of finite element computation is constrained by the difficulty of evaluating high-order nodal basis functions. While most codes rely on explicit formulae for these basis functions, we present a new approach that allows us to construct a general class of finite element basis functions from orthonormal polynomials and evaluate and differentiate them at any points. This approach relies on fundamental ideas from linear algebra and is implemented in Python using several object-oriented and functional programming techniques. (Source:

This software is also peer reviewed by journal TOMS.

References in zbMATH (referenced in 31 articles , 1 standard article )

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  1. Farrell, Patrick E.; Mitchell, Lawrence; Wechsung, Florian: An augmented Lagrangian preconditioner for the 3D stationary incompressible Navier-Stokes equations at High Reynolds number (2019)
  2. Homolya, Miklós; Mitchell, Lawrence; Luporini, Fabio; Ham, David A.: TSFC: a structure-preserving form compiler (2018)
  3. Kirby, Robert C.; Mitchell, Lawrence: Solver composition across the PDE/linear algebra barrier (2018)
  4. Chan, Jesse; Warburton, T.: On the penalty stabilization mechanism for upwind discontinuous Galerkin formulations of first order hyperbolic systems (2017)
  5. Maddison, J. R.; Hiester, H. R.: Optimal constrained interpolation in mesh-adaptive finite element modeling (2017)
  6. Miklos Homolya, Lawrence Mitchell, Fabio Luporini, David A. Ham: TSFC: a structure-preserving form compiler (2017) arXiv
  7. Rathgeber, Florian; Ham, David A.; Mitchell, Lawrence; Lange, Michael; Luporini, Fabio; Mcrae, Andrew T. T.; Bercea, Gheorghe-Teodor; Markall, Graham R.; Kelly, Paul H. J.: Firedrake, automating the finite element method by composing abstractions (2017)
  8. Robert C. Kirby, Lawrence Mitchell: Solver composition across the PDE/linear algebra barrier (2017) arXiv
  9. Yamazaki, Hiroe; Shipton, Jemma; Cullen, Michael J. P.; Mitchell, Lawrence; Cotter, Colin J.: Vertical slice modelling of nonlinear Eady waves using a compatible finite element method (2017)
  10. Lange, Michael; Mitchell, Lawrence; Knepley, Matthew G.; Gorman, Gerard J.: Efficient mesh management in firedrake using PETSc DMPlex (2016)
  11. McRae, A. T. T.; Bercea, G.-T.; Mitchell, L.; Ham, D. A.; Cotter, C. J.: Automated generation and symbolic manipulation of tensor product finite elements (2016)
  12. Mitchell, Lawrence; Müller, Eike Hermann: High level implementation of geometric multigrid solvers for finite element problems: applications in atmospheric modelling (2016)
  13. Farrell, P. E.; Cotter, C. J.; Funke, S. W.: A framework for the automation of generalized stability theory (2014)
  14. Rognes, Marie E.; Logg, Anders: Automated goal-oriented error control. I: Stationary variational problems (2013)
  15. Russell, Francis P.; Kelly, Paul H. J.: Optimized code generation for finite element local assembly using symbolic manipulation (2013)
  16. Dehghan, Mehdi; Sabouri, Mania: A spectral element method for solving the Pennes bioheat transfer equation by using triangular and quadrilateral elements (2012)
  17. Hale, J. S.; Baiz, P. M.: A locking-free meshfree method for the simulation of shear-deformable plates based on a mixed variational formulation (2012)
  18. Alnæs, Martin Sandve; Mardal, Kent-André: On the efficiency of symbolic computations combined with code generation for finite element methods (2010)
  19. Logg, Anders; Wells, Garth N.: DOLFIN: automated finite element computing (2010)
  20. Long, Kevin; Kirby, Robert; Van Bloemen Waanders, Bart: Unified embedded parallel finite element computations via software-based Fréchet differentiation (2010)

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