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:

A simple modification to mitigate locking in conforming FEM for nearly incompressible elasticity

K. Mustapha, W. Mclean, J. Dick and Q.T. Le Gia
Applied Numerical Mathematics 221 18 (2026)
https://doi.org/10.1016/j.apnum.2025.10.017

H(curl)-based approximation of the Stokes problem with weakly enforced no-slip boundary conditions

Wietse M. Boon, Wouter Tonnon and Enrico Zampa
Computer Methods in Applied Mechanics and Engineering 448 118484 (2026)
https://doi.org/10.1016/j.cma.2025.118484

The Lowest-Order Stabilized Virtual Element Method for the Evolutionary Navier-Stokes Equations with Small Viscosity

Xin Liu, Qixuan Song, Rui Zhang and Zhangxin Chen
Journal of Scientific Computing 106 (2) (2026)
https://doi.org/10.1007/s10915-026-03181-3

Superconvergence of the enriched rotated Q1 nonconforming finite element for the Stokes problem based on a cross-correction scheme

Mingxia Li, Shipeng Mao and Shangyou Zhang
Communications in Nonlinear Science and Numerical Simulation 155 109595 (2026)
https://doi.org/10.1016/j.cnsns.2025.109595

Efficient, accurate, and robust penalty-projection algorithm for parameterized stochastic Navier-Stokes flow problems

Neethu Suma Raveendran, Md. Abdul Aziz, Sivaguru S. Ravindran and Muhammad Mohebujjaman
Applied Numerical Mathematics 223 235 (2026)
https://doi.org/10.1016/j.apnum.2026.01.010

An Augmented Lagrangian Preconditioner for the Control of the Navier–Stokes Equations

Santolo Leveque, Michele Benzi and Patrick E. Farrell
SIAM Journal on Scientific Computing 47 (5) A2431 (2025)
https://doi.org/10.1137/24M1683354

A Macro‐Bubble Enriched Divergence‐Free Finite Element on Quadrilateral Meshes

Hongling Hu, Ziqing Xie and Shangyou Zhang
Numerical Methods for Partial Differential Equations 41 (6) (2025)
https://doi.org/10.1002/num.70053

Stability estimates for solving Stokes problem with nonconforming finite elements

Erell Jamelot
Comptes Rendus. Mathématique 363 (G2) 115 (2025)
https://doi.org/10.5802/crmath.707

New Crouzeix-Raviart elements of even degree: theoretical aspects, numerical performance and applications to the Stokes’ equations

A Bressan, L Mascotto and M Mosconi
IMA Journal of Numerical Analysis (2025)
https://doi.org/10.1093/imanum/draf091

A Non‐Dissipative, Energy‐Conserving, Arbitrary High‐Order Numerical Method and Its Efficient Implementation for Incompressible Flow Simulation in Complex Geometries

Sreevatsa Anantharamu and Krishnan Mahesh
International Journal for Numerical Methods in Fluids 97 (4) 503 (2025)
https://doi.org/10.1002/fld.5369

Stabilizing the Scott-Vogelius elements by Guzman-Neilan bubble functions on triangular meshes

Shangyou Zhang
Journal of Applied Mathematics and Computing 71 (3) 3625 (2025)
https://doi.org/10.1007/s12190-025-02373-8

On the necessity of the inf-sup condition for a mixed finite element formulation

Fleurianne Bertrand and Daniele Boffi
IMA Journal of Numerical Analysis 45 (1) 1 (2025)
https://doi.org/10.1093/imanum/drae002

Robust error analysis of stabilized linear EMAC-ESAV finite element schemes for the incompressible Navier-Stokes equations

Rihui Lan, Mengyao Liu and Lili Ju
Mathematics of Computation (2025)
https://doi.org/10.1090/mcom/4087

Pressure-robust finite element discretizations of the nonlinear Stokes equations

Lars Diening, Adrian Hirn, Christian Kreuzer and Pietro Zanotti
Mathematical Models and Methods in Applied Sciences 35 (12) 2661 (2025)
https://doi.org/10.1142/S0218202525500484

An incompressibility, divB=0 preserving, current density, helicity, energy-conserving finite element method for incompressible MHD systems

Shipeng Mao and Ruijie Xi
Journal of Computational Physics 538 114130 (2025)
https://doi.org/10.1016/j.jcp.2025.114130

A new T-compatibility condition and its application to the discretization of the damped time-harmonic Galbrun’s equation

Martin Halla, Christoph Lehrenfeld and Paul Stocker
IMA Journal of Numerical Analysis (2025)
https://doi.org/10.1093/imanum/draf071

Rectangular divergence-free finite elements for axisymmetric Stokes equations

Xuefeng Liu, Ran Zhang, Shangyou Zhang and Zhimin Zhang
Journal of Scientific Computing 105 (2) (2025)
https://doi.org/10.1007/s10915-025-03094-7

Exact integration for singular Zienkiewicz and Guzmán–Neilan finite elements with implementation

Lars Diening, Johannes Storn and Tabea Tscherpel
Computers & Mathematics with Applications 191 60 (2025)
https://doi.org/10.1016/j.camwa.2025.04.019

Penalization of stationary Navier–Stokes equations and applications in topology optimization

Cornel Marius Murea and Dan Tiba
Japan Journal of Industrial and Applied Mathematics 42 (1) 289 (2025)
https://doi.org/10.1007/s13160-024-00676-0

Hybridizable symmetric stress elements on the barycentric refinement in arbitrary dimensions

Long Chen and Xuehai Huang
Mathematics of Computation (2025)
https://doi.org/10.1090/mcom/4180

Multiscale Hybrid-Mixed Methods for the Stokes and Brinkman Equations—A Priori Analysis

Rodolfo Araya, Christopher Harder, Abner H. Poza and Frédéric Valentin
SIAM Journal on Numerical Analysis 63 (2) 588 (2025)
https://doi.org/10.1137/24M1649368

Low regularity error estimates of three pressure-robust discontinuous Galerkin methods for stokes equations

Yuping Zeng and Shangyou Zhang
ESAIM: Mathematical Modelling and Numerical Analysis 59 (2) 873 (2025)
https://doi.org/10.1051/m2an/2025010

A nonconforming P3+B4 and discontinuous P2 mixed finite element on tetrahedral grids

Xuejun Xu and Shangyou Zhang
Advances in Computational Mathematics 51 (4) (2025)
https://doi.org/10.1007/s10444-025-10244-w

Conforming P3 Divergence-Free Finite Elements for the Stokes Equations on Subquadrilateral Triangular Meshes

Shangyou Zhang
Communications on Applied Mathematics and Computation 7 (2) 426 (2025)
https://doi.org/10.1007/s42967-023-00335-0

Two Conjectures on the Stokes Complex in Three Dimensions on Freudenthal Meshes

Patrick E. Farrell, Lawrence Mitchell and L. Ridgway Scott
SIAM Journal on Scientific Computing 46 (2) A629 (2024)
https://doi.org/10.1137/22M1533943

A pressure-robust numerical scheme for the Stokes equations based on the WOPSIP DG approach

Yuping Zeng, Liuqiang Zhong, Feng Wang, Shangyou Zhang and Mingchao Cai
Journal of Computational and Applied Mathematics 445 115819 (2024)
https://doi.org/10.1016/j.cam.2024.115819

Computing \(\boldsymbol{H}^{\boldsymbol{2}}\)-Conforming Finite Element Approximations Without Having to Implement \(\boldsymbol{C}^{\boldsymbol{1}}\)-Elements

Mark Ainsworth and Charles Parker
SIAM Journal on Scientific Computing 46 (4) A2398 (2024)
https://doi.org/10.1137/23M1615486

A locally calculable P3‐pressure in a decoupled method for incompressible Stokes equations

Chunjae Park
Numerical Methods for Partial Differential Equations 40 (5) (2024)
https://doi.org/10.1002/num.23101

A DG Method for the Stokes Equations on Tensor Product Meshes with $$[P_k]^d-P_{k-1}$$ Element

Lin Mu, Xiu Ye, Shangyou Zhang and Peng Zhu
Communications on Applied Mathematics and Computation 6 (4) 2431 (2024)
https://doi.org/10.1007/s42967-022-00243-9

Dimensions of Exactly Divergence-Free Finite Element Spaces in 3D

L. Ridgway Scott and Tabea Tscherpel
SIAM Journal on Scientific Computing 46 (2) A1102 (2024)
https://doi.org/10.1137/22M1544579

On the convergence of 2D P4+$$ {P}_{4+} $$ triangular and 3D P6+$$ {P}_{6+} $$ tetrahedral divergence‐free finite elements

Shangyou Zhang
Numerical Methods for Partial Differential Equations 40 (4) (2024)
https://doi.org/10.1002/num.23088

Neilan's divergence‐free finite elements for Stokes equations on tetrahedral grids

Shangyou Zhang
Numerical Methods for Partial Differential Equations 40 (1) (2024)
https://doi.org/10.1002/num.23055

Reliable chaotic transition in incompressible fluid simulations

Henry von Wahl and L. Ridgway Scott
Advances in Computational Science and Engineering 2 (3) 202 (2024)
https://doi.org/10.3934/acse.2024011

The pressure-wired Stokes element: a mesh-robust version of the Scott–Vogelius element

Benedikt Gräßle, Nis-Erik Bohne and Stefan Sauter
Numerische Mathematik 156 (5) 1781 (2024)
https://doi.org/10.1007/s00211-024-01430-x

A class of space–time discretizations for the stochastic p-Stokes system

Kim-Ngan Le and Jörn Wichmann
Stochastic Processes and their Applications 177 104443 (2024)
https://doi.org/10.1016/j.spa.2024.104443

A General Degree Divergence-Free Finite Element Method for the Two-Dimensional Stokes Problem on Smooth Domains

Rebecca Durst and Michael Neilan
Journal of Scientific Computing 101 (2) (2024)
https://doi.org/10.1007/s10915-024-02674-3

Analysis of a class of globally divergence-free HDG methods for stationary Navier-Stokes equations

Gang Chen and Xiaoping Xie
Science China Mathematics 67 (5) 1133 (2024)
https://doi.org/10.1007/s11425-022-2077-7

Pressure-robust L2(Ω) error analysis for Raviart–Thomas enriched Scott–Vogelius pairs

Volker John, Xu Li and Christian Merdon
Applied Mathematics Letters 156 109138 (2024)
https://doi.org/10.1016/j.aml.2024.109138

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. Faria
Applied Mathematics and Computation 470 128587 (2024)
https://doi.org/10.1016/j.amc.2024.128587

A Tangential and Penalty-Free Finite Element Method for the Surface Stokes Problem

Alan Demlow and Michael Neilan
SIAM Journal on Numerical Analysis 62 (1) 248 (2024)
https://doi.org/10.1137/23M1583995

Quadratic and cubic Lagrange finite elements for mixed Laplace eigenvalue problems on criss-cross meshes

Kaibo Hu, Jiguang Sun and Qian Zhang
Results in Applied Mathematics 23 100480 (2024)
https://doi.org/10.1016/j.rinam.2024.100480

Inf–sup stabilized Scott–Vogelius pairs on general shape-regular simplicial grids by Raviart–Thomas enrichment

Volker John, Xu Li, Christian Merdon and Hongxing Rui
Mathematical Models and Methods in Applied Sciences 34 (05) 919 (2024)
https://doi.org/10.1142/S0218202524500180

A P 2 H-Div-Nonconforming-H-Curl Finite Element for the Stokes Equations on Triangular Meshes

Yunqing Huang, Xuejun Xu and Shangyou Zhang
Computational Methods in Applied Mathematics (2024)
https://doi.org/10.1515/cmam-2024-0060

A fully conservative and shift-invariant formulation for Galerkin discretizations of incompressible variable density flow

Lukas Lundgren and Murtazo Nazarov
Journal of Computational Physics 113086 (2024)
https://doi.org/10.1016/j.jcp.2024.113086

A Modified Rotated-$$Q_1$$ Finite Element for the Stokes Equations on Quadrilateral and Hexahedral Meshes

Liwei Xu, Xuejun Xu and Shangyou Zhang
Journal of Scientific Computing 99 (1) (2024)
https://doi.org/10.1007/s10915-024-02477-6

A pressure-robust mixed finite element method for the coupled Stokes–Darcy problem

Deyong Lv and Hongxing Rui
Journal of Computational and Applied Mathematics 436 115444 (2024)
https://doi.org/10.1016/j.cam.2023.115444

Statically Condensed Iterated Penalty Method for High Order Finite Element Discretizations of Incompressible Flow

Mark Ainsworth and Charles Parker
SIAM Journal on Scientific Computing 45 (6) A3095 (2023)
https://doi.org/10.1137/22M1541368

Convergence of Lagrange finite elements for the Maxwell eigenvalue problem in two dimensions

Daniele Boffi, Johnny Guzmán and Michael Neilan
IMA Journal of Numerical Analysis 43 (2) 663 (2023)
https://doi.org/10.1093/imanum/drab104

Nonconforming Finite Element Methods of Order Two and Order Three for the Stokes Flow in Three Dimensions

Wei Chen, Jun Hu and Min Zhang
Journal of Scientific Computing 97 (1) (2023)
https://doi.org/10.1007/s10915-023-02317-z

A subspace of linear nonconforming finite element for nearly incompressible elasticity and Stokes flow

Shangyou Zhang
Journal of Numerical Mathematics 31 (3) 157 (2023)
https://doi.org/10.1515/jnma-2022-0010

Theoretical analysis and construction of numerical method for solving the Navier–Stokes equations in rotation form with corner singularity

Viktor A. Rukavishnikov and Alexey V. Rukavishnikov
Journal of Computational and Applied Mathematics 429 115218 (2023)
https://doi.org/10.1016/j.cam.2023.115218

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. Wells
Computer Methods in Applied Mechanics and Engineering 417 116493 (2023)
https://doi.org/10.1016/j.cma.2023.116493

Analysis of weakly symmetric mixed finite elements for elasticity

Philip Lederer and Rolf Stenberg
Mathematics of Computation 93 (346) 523 (2023)
https://doi.org/10.1090/mcom/3865

A stable and $$H^1$$-conforming divergence-free finite element pair for the Stokes problem using isoparametric mappings

Michael Neilan and M. Baris Otus
Calcolo 60 (3) (2023)
https://doi.org/10.1007/s10092-023-00531-7

A continuum and computational framework for viscoelastodynamics: II. Strain-driven and energy–momentum consistent schemes

Ju Liu and Jiashen Guan
Computer Methods in Applied Mechanics and Engineering 417 116308 (2023)
https://doi.org/10.1016/j.cma.2023.116308

Finite element de Rham and Stokes complexes in three dimensions

Long Chen and Xuehai Huang
Mathematics of Computation 93 (345) 55 (2023)
https://doi.org/10.1090/mcom/3859

Analysis of divergence free conforming virtual elements for the Brinkman problem

Xuehai Huang and Feng Wang
Mathematical Models and Methods in Applied Sciences 33 (06) 1245 (2023)
https://doi.org/10.1142/S021820252350029X

A cutFEM divergence–free discretization for the stokes problem

Haoran Liu, Michael Neilan and Maxim Olshanskii
ESAIM: Mathematical Modelling and Numerical Analysis 57 (1) 143 (2023)
https://doi.org/10.1051/m2an/2022072

A grad‐div stabilized method using the Jacobi iteration for the thermally coupled incompressible magnetohydrodynamic system

Shuaijun Liu and Pengzhan Huang
ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik 103 (6) (2023)
https://doi.org/10.1002/zamm.202200362

To ℘ or not to p – the mixed displacement–pressure p, versus the higher order ℘ displacement finite element formulation, for nearly incompressible linear elasticity

Adam Zdunek and Waldemar Rachowicz
Computers & Mathematics with Applications 148 313 (2023)
https://doi.org/10.1016/j.camwa.2023.08.025

A low-order divergence-free H(div)-conforming finite element method for Stokes flows

Xu Li and Hongxing Rui
IMA Journal of Numerical Analysis 42 (4) 3711 (2022)
https://doi.org/10.1093/imanum/drab080

A locking-free P0 finite element method for linear elasticity equations on polytopal partitions

Yujie Liu and Junping Wang
IMA Journal of Numerical Analysis 42 (4) 3464 (2022)
https://doi.org/10.1093/imanum/drab057

Numerical Analysis of a Discontinuous Galerkin Method for the Borrvall--Petersson Topology Optimization Problem

Ioannis P. A. Papadopoulos
SIAM Journal on Numerical Analysis 60 (5) 2538 (2022)
https://doi.org/10.1137/21M1438943

Analysis of divergence-free 𝐻¹ conforming FEM with IMEX-SAV scheme for the Navier-Stokes equations at high Reynolds number

Yongbin Han, Yanren Hou and Min Zhang
Mathematics of Computation 92 (340) 557 (2022)
https://doi.org/10.1090/mcom/3790

Energy norm analysis of exactly symmetric mixed finite elements for linear elasticity

Philip Lederer and Rolf Stenberg
Mathematics of Computation 92 (340) 583 (2022)
https://doi.org/10.1090/mcom/3784

A Pointwise Conservative Method for Thermochemical Convection Under the Compressible Anelastic Liquid Approximation

Nathan Sime, Cian R. Wilson and Peter E. van Keken
Geochemistry, Geophysics, Geosystems 23 (2) (2022)
https://doi.org/10.1029/2021GC009922

A posteriori error analysis of Banach spaces-based fully-mixed finite element methods for Boussinesq-type models

Gabriel N. Gatica, Cristian Inzunza, Ricardo Ruiz-Baier and Felipe Sandoval
Journal of Numerical Mathematics 30 (4) 325 (2022)
https://doi.org/10.1515/jnma-2021-0101

A low-degree strictly conservative finite element method for incompressible flows on general triangulations

Huilan Zeng, Chen-Song Zhang and Shuo Zhang
The SMAI Journal of computational mathematics 8 225 (2022)
https://doi.org/10.5802/smai-jcm.85

Note on the effect of grad-div stabilization on calculating drag and lift coefficients

Yasasya Batugedara and Kyle J. Schwiebert
Applied Mathematics and Computation 434 127434 (2022)
https://doi.org/10.1016/j.amc.2022.127434

Crouzeix-Raviart triangular elements are inf-sup stable

Carsten Carstensen and Stefan Sauter
Mathematics of Computation 91 (337) 2041 (2022)
https://doi.org/10.1090/mcom/3742

On the inf-sup stability of Crouzeix-Raviart Stokes elements in 3D

Stefan Sauter and Céline Torres
Mathematics of Computation 92 (341) 1033 (2022)
https://doi.org/10.1090/mcom/3793

Unlocking the secrets of locking: Finite element analysis in planar linear elasticity

Mark Ainsworth and Charles Parker
Computer Methods in Applied Mechanics and Engineering 395 115034 (2022)
https://doi.org/10.1016/j.cma.2022.115034

Low-order divergence-free approximations for the Stokes problem on Worsey–Farin and Powell–Sabin splits

Maurice Fabien, Johnny Guzmán, Michael Neilan and Ahmed Zytoon
Computer Methods in Applied Mechanics and Engineering 390 114444 (2022)
https://doi.org/10.1016/j.cma.2021.114444

Low‐order preconditioning of the Stokes equations

Alexey Voronin, Yunhui He, Scott MacLachlan, Luke N. Olson and Raymond Tuminaro
Numerical Linear Algebra with Applications 29 (3) (2022)
https://doi.org/10.1002/nla.2426

New Numerical Approach for the Steady-State Navier–Stokes Equations with Corner Singularity

Alexey V. Rukavishnikov and Viktor A. Rukavishnikov
International Journal of Computational Methods 19 (09) (2022)
https://doi.org/10.1142/S0219876222500128

Analysis of fully discrete finite element methods for 2D Navier–Stokes equations with critical initial data

Buyang Li, Shu Ma and Yuki Ueda
ESAIM: Mathematical Modelling and Numerical Analysis 56 (6) 2105 (2022)
https://doi.org/10.1051/m2an/2022073

A nonconforming pressure-robust finite element method for the Stokes equations on anisotropic meshes

Thomas Apel, Volker Kempf, Alexander Linke and Christian Merdon
IMA Journal of Numerical Analysis 42 (1) 392 (2022)
https://doi.org/10.1093/imanum/draa097

Partially Discontinuous Nodal Finite Elements for 𝐻(curl) and 𝐻(div)

Jun Hu, Kaibo Hu and Qian Zhang
Computational Methods in Applied Mathematics 22 (3) 613 (2022)
https://doi.org/10.1515/cmam-2022-0053

Computer-assisted proof for the stationary solution existence of the Navier–Stokes equation over 3D domains

Xuefeng Liu, Mitsuhiro T. Nakao and Shin’ichi Oishi
Communications in Nonlinear Science and Numerical Simulation 108 106223 (2022)
https://doi.org/10.1016/j.cnsns.2021.106223

A new DG method for a pure–stress formulation of the Brinkman problem with strong symmetry

Salim Meddahi and Ricardo Ruiz-Baier
Networks and Heterogeneous Media 17 (6) 893 (2022)
https://doi.org/10.3934/nhm.2022031

A pressure robust staggered discontinuous Galerkin method for the Stokes equations

Lina Zhao, Eun-Jae Park and Eric Chung
Computers & Mathematics with Applications 128 163 (2022)
https://doi.org/10.1016/j.camwa.2022.10.019

Robust weak Galerkin finite element solvers for Stokes flow based on a lifting operator

Zhuoran Wang, Ruishu Wang and Jiangguo Liu
Computers & Mathematics with Applications 125 90 (2022)
https://doi.org/10.1016/j.camwa.2022.08.043

A Lowest-Degree Conservative Finite Element Scheme for Incompressible Stokes Problems on General Triangulations

Wenjia Liu and Shuo Zhang
Journal of Scientific Computing 93 (1) (2022)
https://doi.org/10.1007/s10915-022-01974-w

A conforming discontinuous Galerkin finite element method for the Stokes problem on polytopal meshes

Xiu Ye and Shangyou Zhang
International Journal for Numerical Methods in Fluids 93 (6) 1913 (2021)
https://doi.org/10.1002/fld.4959

A Stabilizer-Free, Pressure-Robust, and Superconvergence Weak Galerkin Finite Element Method for the Stokes Equations on Polytopal Mesh

Lin Mu, Xiu Ye and Shangyou Zhang
SIAM Journal on Scientific Computing 43 (4) A2614 (2021)
https://doi.org/10.1137/20M1380405