EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues ESAIM: M2AN, 19 1 (1985) 111-143 Article references

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:

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

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

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

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

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

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

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

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

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

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

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

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 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

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

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 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

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

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

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

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

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 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

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 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

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

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

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

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

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

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

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 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 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

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

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

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

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

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

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

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 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

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

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

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

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

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

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

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

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

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

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

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

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

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

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 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

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

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

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 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

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

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 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

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

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

A Reynolds-robust preconditioner for the Scott-Vogelius discretization of the stationary incompressible Navier-Stokes equations

Patrick E. Farrell, Lawrence Mitchell, L. Ridgway Scott and Florian Wechsung
The SMAI journal of computational mathematics 7 75 (2021)
https://doi.org/10.5802/smai-jcm.72

Explicit a posteriori and a priori error estimation for the finite element solution of Stokes equations

Xuefeng Liu, Mitsuhiro T. Nakao, Chun’guang You and Shin’ichi Oishi
Japan Journal of Industrial and Applied Mathematics 38 (2) 545 (2021)
https://doi.org/10.1007/s13160-020-00449-5

Finite element approximation and preconditioning for anisothermal flow of implicitly-constituted non-Newtonian fluids

Patrick Farrell, Pablo Alexei Gazca Orozco and Endre Süli
Mathematics of Computation 91 (334) 659 (2021)
https://doi.org/10.1090/mcom/3703

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

An Exactly Mass Conserving and Pointwise Divergence Free Velocity Method: Application to Compositional Buoyancy Driven Flow Problems in Geodynamics

Nathan Sime, Jakob M. Maljaars, Cian R. Wilson and Peter E. van Keken
Geochemistry, Geophysics, Geosystems 22 (4) (2021)
https://doi.org/10.1029/2020GC009349

Quasi-Optimal and Pressure Robust Discretizations of the Stokes Equations by Moment- and Divergence-Preserving Operators

Christian Kreuzer, Rüdiger Verfürth and Pietro Zanotti
Computational Methods in Applied Mathematics 21 (2) 423 (2021)
https://doi.org/10.1515/cmam-2020-0023

Mass Conserving Mixed $hp$-FEM Approximations to Stokes Flow. Part I: Uniform Stability

Mark Ainsworth and Charles Parker
SIAM Journal on Numerical Analysis 59 (3) 1218 (2021)
https://doi.org/10.1137/20M1359109

Development of Pressure-Robust Discontinuous Galerkin Finite Element Methods for the Stokes Problem

Lin Mu, Xiu Ye and Shangyou Zhang
Journal of Scientific Computing 89 (1) (2021)
https://doi.org/10.1007/s10915-021-01634-5

Irksome: Automating Runge–Kutta Time-stepping for Finite Element Methods

Patrick E. Farrell, Robert C. Kirby and Jorge Marchena-Menéndez
ACM Transactions on Mathematical Software 47 (4) 1 (2021)
https://doi.org/10.1145/3466168

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

Pressure-robust error estimate of optimal order for the Stokes equations: domains with re-entrant edges and anisotropic mesh grading

Thomas Apel and Volker Kempf
Calcolo 58 (2) (2021)
https://doi.org/10.1007/s10092-021-00402-z

Locking-Free and Gradient-Robust $${\varvec{H}}({{\,\mathrm{{\text {div}}}\,}})$$-Conforming HDG Methods for Linear Elasticity

Guosheng Fu, Christoph Lehrenfeld, Alexander Linke and Timo Streckenbach
Journal of Scientific Computing 86 (3) (2021)
https://doi.org/10.1007/s10915-020-01396-6

The divergence-conforming immersed boundary method: Application to vesicle and capsule dynamics

Hugo Casquero, Carles Bona-Casas, Deepesh Toshniwal, et al.
Journal of Computational Physics 425 109872 (2021)
https://doi.org/10.1016/j.jcp.2020.109872