Hexahedral H(div) and H(curl) finite elements
ESAIM: M2AN, 45 1 (2011) 115-143
Published online: 2010-05-10
Articles citing this article
The Citing articles tool gives a list of articles citing the current article.
The citing articles come from EDP Sciences database, as well as other publishers participating in CrossRef Cited-by Linking Program. You can set up your personal account to receive an email alert each time this article is cited by a new article (see the menu on the right-hand side of the abstract page).
Cited article:
This article has been cited by the following article(s):
A priori verification method for curl‐conforming basis functions in simplices
Adrian Amor‐Martin and Luis E. Garcia‐CastilloMathematical Methods in the Applied Sciences 48 (1) 144 (2025)
https://doi.org/10.1002/mma.10319
A global H(div)-conforming finite element post-processing for stress recovery in nearly incompressible elasticity
G. Taraschi, M.R. Correa, A.S. Pinto and C.O. FariaApplied Mathematics and Computation 470 128587 (2024)
https://doi.org/10.1016/j.amc.2024.128587
A macro BDM H-div mixed finite element on polygonal and polyhedral meshes
Xuejun Xu, Xiu Ye and Shangyou ZhangApplied Numerical Mathematics 206 283 (2024)
https://doi.org/10.1016/j.apnum.2024.08.013
Numerical Algorithms for Divergence-Free Velocity Applications
Giacomo Barbi, Antonio Cervone and Sandro ManservisiMathematics 12 (16) 2514 (2024)
https://doi.org/10.3390/math12162514
A Penalty-Free and Essentially Stabilization-Free DG Method for Convection-Dominated Second-Order Elliptic Problems
Huoyuan Duan and Junhua MaJournal of Scientific Computing 100 (2) (2024)
https://doi.org/10.1007/s10915-024-02615-0
A stabilized finite element method on nonaffine grids for time-harmonic Maxwell’s equations
Zhijie Du and Huoyuan DuanBIT Numerical Mathematics 63 (4) (2023)
https://doi.org/10.1007/s10543-023-00988-6
Second-Order Nédélec Curl-Conforming Hexahedral Element for Computational Electromagnetics
Adrian Amor-Martin and Luis Emilio Garcia-CastilloIEEE Transactions on Antennas and Propagation 71 (1) 859 (2023)
https://doi.org/10.1109/TAP.2022.3216554
A Bochev‐Dohrmann‐Gunzburger stabilized method for Maxwell eigenproblem
Zhijie Du, Huoyuan Duan, Can Wang and Qiuyu ZhangNumerical Methods for Partial Differential Equations 39 (5) 3811 (2023)
https://doi.org/10.1002/num.23026
On pressure robustness and independent determination of displacement and pressure in incompressible linear elasticity
Adam Zdunek, Michael Neunteufel and Waldemar RachowiczComputer Methods in Applied Mechanics and Engineering 403 115714 (2023)
https://doi.org/10.1016/j.cma.2022.115714
Design and analysis of an exactly divergence-free hybridised discontinuous Galerkin method for incompressible flows on meshes with quadrilateral cells
Joseph P. Dean, Sander Rhebergen and Garth N. WellsComputer Methods in Applied Mechanics and Engineering 417 116493 (2023)
https://doi.org/10.1016/j.cma.2023.116493
1 (2022)
https://doi.org/10.23919/MIKON54314.2022.9924952
A Div FOSLS Method Suitable for Quadrilateral RT and Hexahedral RTN $$H(\textrm{div})$$-elements
Huoyuan Duan, Can Wang and Zhijie DuJournal of Scientific Computing 93 (3) (2022)
https://doi.org/10.1007/s10915-022-02043-y
An Interpolated Galerkin Finite Element Method for the Poisson Equation
Tatyana Sorokina and Shangyou ZhangJournal of Scientific Computing 92 (2) (2022)
https://doi.org/10.1007/s10915-022-01903-x
A lowest-degree quasi-conforming finite element de Rham complex on general quadrilateral grids by piecewise polynomials
Qimeng Quan, Xia Ji and Shuo ZhangCalcolo 59 (1) (2022)
https://doi.org/10.1007/s10092-021-00447-0
1 (2021)
https://doi.org/10.23919/IEEECONF54431.2021.9598379
Mixed Finite Element Method with Gauss's Law Enforced for the Maxwell Eigenproblem
Huoyuan Duan, Junhua Ma and Jun ZouSIAM Journal on Scientific Computing 43 (6) A3677 (2021)
https://doi.org/10.1137/20M1350753
Approximation Theory XVI
Tatyana Sorokina and Shangyou ZhangSpringer Proceedings in Mathematics & Statistics, Approximation Theory XVI 336 237 (2021)
https://doi.org/10.1007/978-3-030-57464-2_13
H(div) finite elements based on nonaffine meshes for 3D mixed formulations of flow problems with arbitrary high order accuracy of the divergence of the flux
Philippe Remy Bernard Devloo, Omar Durán, Agnaldo Monteiro Farias and Sônia Maria GomesInternational Journal for Numerical Methods in Engineering 121 (13) 2896 (2020)
https://doi.org/10.1002/nme.6337
A locking-free solver for linear elasticity on quadrilateral and hexahedral meshes based on enrichment of Lagrangian elements
Graham Harper, Ruishu Wang, Jiangguo Liu, Simon Tavener and Ran ZhangComputers & Mathematics with Applications 80 (6) 1578 (2020)
https://doi.org/10.1016/j.camwa.2020.07.014
https://doi.org/10.1002/9781119671688.biblio
Finite-element EM modelling on hexahedral grids with an FD solver as a pre-conditioner
Nikolay Yavich and Michael S ZhdanovGeophysical Journal International 223 (2) 840 (2020)
https://doi.org/10.1093/gji/ggaa341
Construction of $$H({\mathrm{div}})$$ H ( div ) -conforming mixed finite elements on cuboidal hexahedra
Todd Arbogast and Zhen TaoNumerische Mathematik 142 (1) 1 (2019)
https://doi.org/10.1007/s00211-018-0998-7
A multiscale hybrid method for Darcy’s problems using mixed finite element local solvers
Omar Durán, Philippe R.B. Devloo, Sônia M. Gomes and Frédéric ValentinComputer Methods in Applied Mechanics and Engineering 354 213 (2019)
https://doi.org/10.1016/j.cma.2019.05.013
Hybridization and stabilization for hp-finite element methods
Lothar Banz, Jan Petsche and Andreas SchröderApplied Numerical Mathematics 136 66 (2019)
https://doi.org/10.1016/j.apnum.2018.09.017
High-order composite finite element exact sequences based on tetrahedral–hexahedral–prismatic–pyramidal partitions
Philippe R.B. Devloo, Omar Durán, Sônia M. Gomes and Mark AinsworthComputer Methods in Applied Mechanics and Engineering 355 952 (2019)
https://doi.org/10.1016/j.cma.2019.06.022
On a general implementation of h- and p-adaptive curl-conforming finite elements
Marc Olm, Santiago Badia and Alberto F. MartínAdvances in Engineering Software 132 74 (2019)
https://doi.org/10.1016/j.advengsoft.2019.03.006
Large-Scale Scientific Computing
Artur Palha and Marc GerritsmaLecture Notes in Computer Science, Large-Scale Scientific Computing 10665 119 (2018)
https://doi.org/10.1007/978-3-319-73441-5_12
Lowest-Order Weak Galerkin Finite Element Method for Darcy Flow on Convex Polygonal Meshes
Jiangguo Liu, Simon Tavener and Zhuoran WangSIAM Journal on Scientific Computing 40 (5) B1229 (2018)
https://doi.org/10.1137/17M1145677
The THex Algorithm and a Simple Darcy Solver on Hexahedral Meshes
Graham Harper, Jiangguo Liu and Bin ZhengProcedia Computer Science 108 1903 (2017)
https://doi.org/10.1016/j.procs.2017.05.148
Multilevel Balancing Domain Decomposition by Constraints Deluxe Algorithms with Adaptive Coarse Spaces for Flow in Porous Media
Stefano Zampini and Xuemin TuSIAM Journal on Scientific Computing 39 (4) A1389 (2017)
https://doi.org/10.1137/16M1080653
A Mixed Finite Element Method to Solve the EEG Forward Problem
J. Vorwerk, C. Engwer, S. Pursiainen and C. H. WoltersIEEE Transactions on Medical Imaging 36 (4) 930 (2017)
https://doi.org/10.1109/TMI.2016.2624634
Two Families of $H$(div) Mixed Finite Elements on Quadrilaterals of Minimal Dimension
Todd Arbogast and Maicon R. CorreaSIAM Journal on Numerical Analysis 54 (6) 3332 (2016)
https://doi.org/10.1137/15M1013705
3-D magnetotelluric inversion including topography using deformed hexahedral edge finite elements and direct solvers parallelized on SMP computers – Part I: forward problem and parameter Jacobians
M. Kordy, P. Wannamaker, V. Maris, E. Cherkaev and G. HillGeophysical Journal International 204 (1) 74 (2016)
https://doi.org/10.1093/gji/ggv410
Finite element differential forms on curvilinear cubic meshes and their approximation properties
Douglas N. Arnold, Daniele Boffi and Francesca BonizzoniNumerische Mathematik 129 (1) 1 (2015)
https://doi.org/10.1007/s00211-014-0631-3
Implementation of enhanced shape functions for non‐affine elements
Gaëlle Andriamaro, Oleg Davydov and John SimkinIET Science, Measurement & Technology 9 (2) 184 (2015)
https://doi.org/10.1049/iet-smt.2014.0191
Coupling multipoint flux mixed finite element methodswith continuous Galerkin methods for poroelasticity
Mary Wheeler, Guangri Xue and Ivan YotovComputational Geosciences 18 (1) 57 (2014)
https://doi.org/10.1007/s10596-013-9382-y
Locking free quadrilateral continuous/discontinuous finite element methods for the Reissner–Mindlin plate
Peter Hansbo and Mats G. LarsonComputer Methods in Applied Mechanics and Engineering 269 381 (2014)
https://doi.org/10.1016/j.cma.2013.11.004
Divergence-Free $\boldsymbol{\mathcal{H}}(\mathbf{div})$ -Conforming Hierarchical Bases for Magnetohydrodynamics (MHD)
Wei Cai, Jian Wu and Jianguo XinCommunications in Mathematics and Statistics 1 (1) 19 (2013)
https://doi.org/10.1007/s40304-013-0003-9
High-order optimal edge elements for pyramids, prisms and hexahedra
Morgane Bergot and Marc DurufléJournal of Computational Physics 232 (1) 189 (2013)
https://doi.org/10.1016/j.jcp.2012.08.005
44 47 (2013)
https://doi.org/10.1007/978-3-642-36519-5_2
Approximation of H(div) with High-Order Optimal Finite Elements for Pyramids, Prisms and Hexahedra
Morgane Bergot and Marc DurufléCommunications in Computational Physics 14 (5) 1372 (2013)
https://doi.org/10.4208/cicp.120712.080313a
Application of the control volume mixed finite element method to a triangular discretization
R.L. NaffInternational Journal for Numerical Methods in Engineering 89 (7) 846 (2012)
https://doi.org/10.1002/nme.3265
Conforming Hierarchical Basis Functions
M. J. BluckCommunications in Computational Physics 12 (4) 1215 (2012)
https://doi.org/10.4208/cicp.090511.071211a
A multipoint flux mixed finite element method on distorted quadrilaterals and hexahedra
Mary Wheeler, Guangri Xue and Ivan YotovNumerische Mathematik 121 (1) 165 (2012)
https://doi.org/10.1007/s00211-011-0427-7
Analysis and Computation of Compatible Least-Squares Methods for div-curl Equations
Pavel B. Bochev, Kara Peterson and Christopher M. SiefertSIAM Journal on Numerical Analysis 49 (1) 159 (2011)
https://doi.org/10.1137/090772095