DefElement: an encyclopedia of finite element definitions

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Bibliographic Details
Main Authors:	Scroggs, Matthew W., Brubeck, Pablo D., Dean, Joseph P., Dokken, Jørgen S., Marsden, India
Format:	Preprint
Published:	2025
Subjects:	Numerical Analysis
Online Access:	Acceder al recurso
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On the numerical evaluation of wall shear stress using the finite element method
by: Brunátová, Jana, et al.
Published: (2025)

FIAT: improving performance and accuracy for high-order finite elements
by: Brubeck, Pablo D., et al.
Published: (2024)

Accelerated implicitization: Robust fixed-point iterations arising from an explicit scheme
by: Barnafi, Nicolas A., et al.
Published: (2025)

Cohomology of Finite Element Stokes Complexes on Alfeld Splits
by: Brubeck, Pablo D., et al.
Published: (2026)

Achieving Material Robustness via Symmetric Stress Finite Element Discretizations
by: Brubeck, Pablo, et al.
Published: (2026)

Proximal Galerkin for Phase Field Fracture
by: Castillón, Miguel, et al.
Published: (2026)

FIAT: enabling classical and modern macroelements
by: Brubeck, Pablo D., et al.
Published: (2025)

A scalable and robust vertex-star relaxation for high-order FEM
by: Brubeck, Pablo D., et al.
Published: (2021)

Symmetric, Optimization-based, Cross-element Compatible Nodal Distributions for High-order Finite Elements
by: Kaufmann, Julian M., et al.
Published: (2024)

The latent variable proximal point algorithm for variational problems with inequality constraints
by: Dokken, Jørgen S., et al.
Published: (2025)

Evolving finite elements for advection diffusion with an evolving interface
by: Elliott, C. M., et al.
Published: (2022)

Element learning: a systematic approach of accelerating finite element-type methods via machine learning, with applications to radiative transfer
by: Du, Shukai, et al.
Published: (2023)

A sparse hierarchical $hp$-finite element method on disks and annuli
by: Papadopoulos, Ioannis P. A., et al.
Published: (2024)

Superconvergence in finite element method by smoothing
by: Li, Yuwen, et al.
Published: (2026)

Adaptive finite elements for obstacle problems
by: Gustafsson, Tom
Published: (2024)

Towards finite element exterior calculus on manifolds: commuting projections, geometric variational crimes, and approximation errors
by: Licht, Martin W.
Published: (2023)

The Adini finite element on locally refined meshes
by: Gallistl, Dietmar
Published: (2025)

Unfitted finite element interpolated neural networks
by: Li, Wei, et al.
Published: (2025)

Compatible finite element interpolated neural networks
by: Badia, Santiago, et al.
Published: (2024)

Nonnegative moment coordinates on finite element geometries
by: Dieci, Luca, et al.
Published: (2023)

Isoparametric Virtual Element Methods
by: Cangiani, Andrea, et al.
Published: (2024)

Convergence of finite element right-hand-side computation from finite difference data
by: Schoder, Stefan
Published: (2026)

Mixed finite element and TPSA finite volume methods for linearized elasticity and Cosserat materials
by: Nordbotten, Jan Martin, et al.
Published: (2024)

Quantum-assisted hλ-adaptive finite element method
by: Drebotiy, R. H., et al.
Published: (2024)

An Extended Galerkin analysis in finite element exterior calculus
by: Hong, Qingguo, et al.
Published: (2021)

Multiscale finite element method for Stokes-Darcy model
by: Hong, Yachen, et al.
Published: (2024)

Convergent finite elements on arbitrary meshes, the WG method
by: Zhang, Ran, et al.
Published: (2024)

Semi-implicit hybrid finite volume/finite element method for the GPR model of continuum mechanics
by: Busto, Saray, et al.
Published: (2024)

A hybrid finite element/finite difference method for reconstruction of dielectric properties of conductive objects
by: Lindström, Eric, et al.
Published: (2024)

Eigenbounds of symmetric positive definite tensors
by: Nayak, Snigdhashree, et al.
Published: (2026)

A posteriori error bounds for finite element approximations of steady-state mean field games
by: Osborne, Yohance A. P., et al.
Published: (2025)

An ultra-weak three-field finite element formulation for the biharmonic and extended Fisher--Kolmogorov equations
by: Khot, Rekha, et al.
Published: (2026)

Splitting finite element approximations for quasi-static electroporoelasticity equations
by: Liu, Xuan, et al.
Published: (2025)

Convergence analysis of the adaptive stochastic collocation finite element method
by: Bespalov, Alex, et al.
Published: (2024)

Strongly consistent low-dissipation WENO schemes for finite elements
by: Vedral, Joshua, et al.
Published: (2024)

On the best accuracy using the $h$-adaptive finite element refinement
by: Liu, Jie
Published: (2025)

A cut finite element method for the Biot system of poroelasticity
by: Berre, Nanna, et al.
Published: (2025)

Advances on the finite element discretization of fluid-structure interaction problems
by: Alshehri, Najwa, et al.
Published: (2025)

Four-field mixed finite elements for incompressible nonlinear elasticity
by: Badia, Santiago, et al.
Published: (2026)

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