A new family of mixed finite elements in IR3
Numerische Mathematik
Mixed and hybrid finite element methods
Mixed and hybrid finite element methods
A Robust Finite Element Method for Darcy--Stokes Flow
SIAM Journal on Numerical Analysis
Algorithm 839: FIAT, a new paradigm for computing finite element basis functions
ACM Transactions on Mathematical Software (TOMS)
Quadrilateral H(div) Finite Elements
SIAM Journal on Numerical Analysis
Optimizing the Evaluation of Finite Element Matrices
SIAM Journal on Scientific Computing
FEMSTER: An object-oriented class library of high-order discrete differential forms
ACM Transactions on Mathematical Software (TOMS)
Topological Optimization of the Evaluation of Finite Element Matrices
SIAM Journal on Scientific Computing
Optimizing FIAT with level 3 BLAS
ACM Transactions on Mathematical Software (TOMS)
A compiler for variational forms
ACM Transactions on Mathematical Software (TOMS)
Efficient compilation of a class of variational forms
ACM Transactions on Mathematical Software (TOMS)
Geometric Optimization of the Evaluation of Finite Element Matrices
SIAM Journal on Scientific Computing
Benchmarking Domain-Specific Compiler Optimizations for Variational Forms
ACM Transactions on Mathematical Software (TOMS)
Algorithm 884: A Simple Matlab Implementation of the Argyris Element
ACM Transactions on Mathematical Software (TOMS)
ACM Transactions on Mathematical Software (TOMS)
Automated Code Generation for Discontinuous Galerkin Methods
SIAM Journal on Scientific Computing
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In this paper, we discuss how to efficiently evaluate and assemble general finite element variational forms on $H(\mathrm{div})$ and $H(\mathrm{curl})$. The proposed strategy relies on a decomposition of the element tensor into a precomputable reference tensor and a mesh-dependent geometry tensor. Two key points must then be considered: the appropriate mapping of basis functions from a reference element, and the orientation of geometrical entities. To address these issues, we extend here a previously presented representation theorem for affinely mapped elements to Piola-mapped elements. We also discuss a simple numbering strategy that removes the need to contend with directions of facet normals and tangents. The result is an automated, efficient, and easy-to-use implementation that allows a user to specify finite element variational forms on $H(\mathrm{div})$ and $H(\mathrm{curl})$ in close to mathematical notation.