Low-Complexity Finite Element Algorithms for the de Rham Complex on Simplices

DOI10.1137/130927693zbMath1296.65161OpenAlexW2022368757MaRDI QIDQ2875008

Robert C. Kirby

Publication date: 13 August 2014

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/130927693

zbMATH Keywords

algorithmspectral element methodBernstein polynomialsde Rham complexPoisson equationnumerical resultfinite element exterior calculusoptimal complexityMaxwell eigenvalue problem

Mathematics Subject Classification ID

Estimates of eigenvalues in context of PDEs (35P15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Numerical methods for eigenvalue problems for boundary value problems involving PDEs (65N25) Complexity and performance of numerical algorithms (65Y20) Maxwell equations (35Q61)

Related Items

On basis constructions in finite element exterior calculus ⋮ Bernstein-Bézier \(H(\mathrm{curl})\)-conforming finite elements for time-harmonic electromagnetic scattering problems ⋮ Structured Inversion of the Bernstein Mass Matrix ⋮ Fast inversion of the simplicial Bernstein mass matrix ⋮ Bernstein-Bézier bases for tetrahedral finite elements ⋮ A Short Note on a Bernstein--Bezier Basis for the Pyramid ⋮ On high order finite element spaces of differential forms ⋮ Computing the Bézier Control Points of the Lagrangian Interpolant in Arbitrary Dimension ⋮ Subcell flux limiting for high-order Bernstein finite element discretizations of scalar hyperbolic conservation laws

Uses Software

• FEniCS