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 38 articles , 1 standard article )

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  1. Matthew W. Scroggs: Symfem: a symbolic finite element definition library (2021) not zbMATH
  2. Rosales, Rodolfo Ruben; Seibold, Benjamin; Shirokoff, David; Zhou, Dong: High-order finite element methods for a pressure Poisson equation reformulation of the Navier-Stokes equations with electric boundary conditions (2021)
  3. Jahn, Mischa; Montalvo-Urquizo, Jonathan: Modeling and simulation of keyhole-based welding as multi-domain problem using the extended finite element method (2020)
  4. Farrell, Patrick E.; Mitchell, Lawrence; Wechsung, Florian: An augmented Lagrangian preconditioner for the 3D stationary incompressible Navier-Stokes equations at High Reynolds number (2019)
  5. Kirby, Robert C.; Mitchell, Lawrence: Code generation for generally mapped finite elements (2019)
  6. Winovich, Nick; Ramani, Karthik; Lin, Guang: ConvPDE-UQ: convolutional neural networks with quantified uncertainty for heterogeneous elliptic partial differential equations on varied domains (2019)
  7. Homolya, Miklós; Mitchell, Lawrence; Luporini, Fabio; Ham, David A.: TSFC: a structure-preserving form compiler (2018)
  8. Kirby, Robert C.; Mitchell, Lawrence: Solver composition across the PDE/linear algebra barrier (2018)
  9. Chan, Jesse; Warburton, T.: On the penalty stabilization mechanism for upwind discontinuous Galerkin formulations of first order hyperbolic systems (2017)
  10. Maddison, J. R.; Hiester, H. R.: Optimal constrained interpolation in mesh-adaptive finite element modeling (2017)
  11. Miklos Homolya, Lawrence Mitchell, Fabio Luporini, David A. Ham: TSFC: a structure-preserving form compiler (2017) arXiv
  12. 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)
  13. Robert C. Kirby, Lawrence Mitchell: Solver composition across the PDE/linear algebra barrier (2017) arXiv
  14. 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)
  15. Lange, Michael; Mitchell, Lawrence; Knepley, Matthew G.; Gorman, Gerard J.: Efficient mesh management in firedrake using PETSc DMPlex (2016)
  16. 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)
  17. Mitchell, Lawrence; Müller, Eike Hermann: High level implementation of geometric multigrid solvers for finite element problems: applications in atmospheric modelling (2016)
  18. Shao, Xinping; Han, Danfu; Hu, Xianliang: A (p)-version two level spline method for 2D Navier-Stokes equations (2016)
  19. Sabouri, Mania; Dehghan, Mehdi: An efficient implicit spectral element method for time-dependent nonlinear diffusion equations by evaluating integrals at one quadrature point (2015)
  20. Farrell, P. E.; Cotter, C. J.; Funke, S. W.: A framework for the automation of generalized stability theory (2014)

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