Robust Arbitrary Order Mixed Finite Element Methods for the Incompressible Stokes Equations with pressure independent velocity errors
ESAIM: M2AN, 50 1 (2016) 289-309
Published online: 2016-01-28
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):
Low regularity error analysis for an H(div)-conforming discontinuous Galerkin approximation of Stokes problem
Yuping Zeng, Liuqiang Zhong, Feng Wang, Mingchao Cai and Shangyou ZhangJournal of Computational and Applied Mathematics 451 116118 (2024)
https://doi.org/10.1016/j.cam.2024.116118
Inf-sup stabilized Scott–Vogelius pairs on general shape-regular simplicial grids for Navier–Stokes equations
Naveed Ahmed, Volker John, Xu Li and Christian MerdonComputers & Mathematics with Applications 168 148 (2024)
https://doi.org/10.1016/j.camwa.2024.05.034
Pressure-robust finite element scheme for the time-dependent fully coupled Stokes–Darcy-transport problem
Deyong Lv and Hongxing RuiJournal of Computational and Applied Mathematics 451 116089 (2024)
https://doi.org/10.1016/j.cam.2024.116089
A pressure-robust divergence free finite element basis for the Stokes equations
Jay Chu, Xiaozhe Hu and Lin MuElectronic Research Archive 32 (10) 5633 (2024)
https://doi.org/10.3934/era.2024261
A pressure-robust mixed finite element method for the coupled Stokes–Darcy problem
Deyong Lv and Hongxing RuiJournal of Computational and Applied Mathematics 436 115444 (2024)
https://doi.org/10.1016/j.cam.2023.115444
Analysis of a $$\varvec{P}_1\oplus \varvec{RT}_0$$ finite element method for linear elasticity with Dirichlet and mixed boundary conditions
Hongpeng Li, Xu Li and Hongxing RuiAdvances in Computational Mathematics 50 (1) (2024)
https://doi.org/10.1007/s10444-024-10107-w
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 CaiJournal of Computational and Applied Mathematics 445 115819 (2024)
https://doi.org/10.1016/j.cam.2024.115819
Tensor-Product Space-Time Goal-Oriented Error Control and Adaptivity With Partition-of-Unity Dual-Weighted Residuals for Nonstationary Flow Problems
Julian Roth, Jan Philipp Thiele, Uwe Köcher and Thomas WickComputational Methods in Applied Mathematics 24 (1) 185 (2024)
https://doi.org/10.1515/cmam-2022-0200
Gradient-Robust Hybrid DG Discretizations for the Compressible Stokes Equations
P. L. Lederer and C. MerdonJournal of Scientific Computing 100 (2) (2024)
https://doi.org/10.1007/s10915-024-02605-2
Pressure-robust approximation of the incompressible Navier–Stokes equations in a rotating frame of reference
Medine Demir and Volker JohnBIT Numerical Mathematics 64 (4) (2024)
https://doi.org/10.1007/s10543-024-01037-6
FINITE ELEMENT ANALYSIS OF LINEARLY EXTRAPOLATED BLENDED BACKWARD DIFFERENCE FORMULA (BLEBDF) FOR THE NATURAL CONVECTION FLOWS
Merve Ak and Mine AkbasMaltepe Journal of Mathematics 6 (2) 61 (2024)
https://doi.org/10.47087/mjm.1477504
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 ZhuCommunications on Applied Mathematics and Computation 6 (4) 2431 (2024)
https://doi.org/10.1007/s42967-022-00243-9
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
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 RachowiczComputers & Mathematics with Applications 148 313 (2023)
https://doi.org/10.1016/j.camwa.2023.08.025
Pressure-Robustness in the Context of Optimal Control
Christian Merdon and Winnifried WollnerSIAM Journal on Control and Optimization 61 (1) 342 (2023)
https://doi.org/10.1137/22M1482603
Three interior penalty DG methods for stationary incompressible magnetohydrodynamics
Huayi Huang, Yunqing Huang and Xiaojing DongJournal of Computational and Applied Mathematics 425 115030 (2023)
https://doi.org/10.1016/j.cam.2022.115030
Gradient Robust Mixed Methods for Nearly Incompressible Elasticity
Seshadri R. Basava and Winnifried WollnerJournal of Scientific Computing 95 (3) (2023)
https://doi.org/10.1007/s10915-023-02227-0
A pressure-robust virtual element method for the Navier-Stokes problem on polygonal mesh
Ying Wang, Gang Wang and Yue ShenComputers & Mathematics with Applications 131 124 (2023)
https://doi.org/10.1016/j.camwa.2022.12.013
An EMA-conserving, pressure-robust and Re-semi-robust method with A robust reconstruction method for Navier–Stokes
Xu Li and Hongxing RuiESAIM: Mathematical Modelling and Numerical Analysis 57 (2) 467 (2023)
https://doi.org/10.1051/m2an/2022093
Nonconforming Finite Element Methods of Order Two and Order Three for the Stokes Flow in Three Dimensions
Wei Chen, Jun Hu and Min ZhangJournal of Scientific Computing 97 (1) (2023)
https://doi.org/10.1007/s10915-023-02317-z
A Modified Convective Formulation in Navier–Stokes Simulations
Xu Li and Hongxing RuiJournal of Scientific Computing 96 (3) (2023)
https://doi.org/10.1007/s10915-023-02286-3
A pressure‐robust weak Galerkin finite element method for Navier–Stokes equations
Lin MuNumerical Methods for Partial Differential Equations 39 (3) 2327 (2023)
https://doi.org/10.1002/num.22969
Divergence-preserving reconstructions on polygons and a really pressure-robust virtual element method for the Stokes problem
Derk Frerichs and Christian MerdonIMA Journal of Numerical Analysis 42 (1) 597 (2022)
https://doi.org/10.1093/imanum/draa073
Guaranteed upper bounds for the velocity error of pressure-robust Stokes discretisations
Philip L. Lederer and Christian MerdonJournal of Numerical Mathematics 30 (4) 267 (2022)
https://doi.org/10.1515/jnma-2021-0078
A pressure robust staggered discontinuous Galerkin method for the Stokes equations
Lina Zhao, Eun-Jae Park and Eric ChungComputers & Mathematics with Applications 128 163 (2022)
https://doi.org/10.1016/j.camwa.2022.10.019
Analysis and computation of a pressure-robust method for the rotation form of the incompressible Navier–Stokes equations with high-order finite elements
Di Yang, Yinnian He and Yarong ZhangComputers & Mathematics with Applications 112 1 (2022)
https://doi.org/10.1016/j.camwa.2022.02.017
A low-order divergence-free H(div)-conforming finite element method for Stokes flows
Xu Li and Hongxing RuiIMA Journal of Numerical Analysis 42 (4) 3711 (2022)
https://doi.org/10.1093/imanum/drab080
A nonconforming pressure-robust finite element method for the Stokes equations on anisotropic meshes
Thomas Apel, Volker Kempf, Alexander Linke and Christian MerdonIMA Journal of Numerical Analysis 42 (1) 392 (2022)
https://doi.org/10.1093/imanum/draa097
Non-standard Discretisation Methods in Solid Mechanics
Seshadri Basava, Katrin Mang, Mirjam Walloth, Thomas Wick and Winnifried WollnerLecture Notes in Applied and Computational Mechanics, Non-standard Discretisation Methods in Solid Mechanics 98 191 (2022)
https://doi.org/10.1007/978-3-030-92672-4_8
New stabilized P1 × P0 finite element methods for nearly inviscid and incompressible flows
Yuwen Li and Ludmil T. ZikatanovComputer Methods in Applied Mechanics and Engineering 393 114815 (2022)
https://doi.org/10.1016/j.cma.2022.114815
Modular grad-div stabilization for the incompressible non-isothermal fluid flows
Mine Akbas and Leo G. RebholzApplied Mathematics and Computation 393 125748 (2021)
https://doi.org/10.1016/j.amc.2020.125748
Viscosity robust weak Galerkin finite element methods for Stokes problems
Bin Wang and Lin MuElectronic Research Archive 29 (1) 1881 (2021)
https://doi.org/10.3934/era.2020096
Locking-Free and Gradient-Robust $${\varvec{H}}({{\,\mathrm{{\text {div}}}\,}})$$-Conforming HDG Methods for Linear Elasticity
Guosheng Fu, Christoph Lehrenfeld, Alexander Linke and Timo StreckenbachJournal of Scientific Computing 86 (3) (2021)
https://doi.org/10.1007/s10915-020-01396-6
Development of Pressure-Robust Discontinuous Galerkin Finite Element Methods for the Stokes Problem
Lin Mu, Xiu Ye and Shangyou ZhangJournal of Scientific Computing 89 (1) (2021)
https://doi.org/10.1007/s10915-021-01634-5
A pressure-robust virtual element method for the Stokes problem
Gang Wang, Lin Mu, Ying Wang and Yinnian HeComputer Methods in Applied Mechanics and Engineering 382 113879 (2021)
https://doi.org/10.1016/j.cma.2021.113879
An a priori error analysis for a projection based variational multiscale finite element method for Oseen problems in a time-dependent domain
Birupaksha Pal and Sashikumaar GanesanComputers & Mathematics with Applications 82 130 (2021)
https://doi.org/10.1016/j.camwa.2020.10.025
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 ZhangSIAM Journal on Scientific Computing 43 (4) A2614 (2021)
https://doi.org/10.1137/20M1380405
A Hellan--Herrmann--Johnson-like Method for the Stream Function Formulation of the Stokes Equations in Two and Three Space Dimensions
Philip L. LedererSIAM Journal on Numerical Analysis 59 (1) 503 (2021)
https://doi.org/10.1137/20M1338034
A Pressure-Robust Discretization of Oseen's Equation Using Stabilization in the Vorticity Equation
Naveed Ahmed, Gabriel R. Barrenechea, Erik Burman, et al.SIAM Journal on Numerical Analysis 59 (5) 2746 (2021)
https://doi.org/10.1137/20M1351230
Finite element approximation and preconditioning for anisothermal flow of implicitly-constituted non-Newtonian fluids
Patrick Farrell, Pablo Alexei Gazca Orozco and Endre SüliMathematics of Computation 91 (334) 659 (2021)
https://doi.org/10.1090/mcom/3703
Quasi-optimal and pressure-robust discretizations of the Stokes equations by new augmented Lagrangian formulations
Christian Kreuzer and Pietro ZanottiIMA Journal of Numerical Analysis 40 (4) 2553 (2020)
https://doi.org/10.1093/imanum/drz044
Fluids Under Pressure
Volker John, Petr Knobloch and Ulrich WilbrandtAdvances in Mathematical Fluid Mechanics, Fluids Under Pressure 483 (2020)
https://doi.org/10.1007/978-3-030-39639-8_6
Pressure Robust Weak Galerkin Finite Element Methods for Stokes Problems
Lin MuSIAM Journal on Scientific Computing 42 (3) B608 (2020)
https://doi.org/10.1137/19M1266320
Finite Volumes for Complex Applications IX - Methods, Theoretical Aspects, Examples
Alexander Linke and Christian MerdonSpringer Proceedings in Mathematics & Statistics, Finite Volumes for Complex Applications IX - Methods, Theoretical Aspects, Examples 323 103 (2020)
https://doi.org/10.1007/978-3-030-43651-3_7
Divergence‐free tangential finite element methods for incompressible flows on surfaces
Philip L. Lederer, Christoph Lehrenfeld and Joachim SchöberlInternational Journal for Numerical Methods in Engineering 121 (11) 2503 (2020)
https://doi.org/10.1002/nme.6317
A mass conserving mixed stress formulation for the Stokes equations
Joachim Schöberl, Philip L Lederer and Jay GopalakrishnanIMA Journal of Numerical Analysis 40 (3) 1838 (2020)
https://doi.org/10.1093/imanum/drz022
A Pressure-Robust Embedded Discontinuous Galerkin Method for the Stokes Problem by Reconstruction Operators
Philip L. Lederer and Sander RhebergenSIAM Journal on Numerical Analysis 58 (5) 2915 (2020)
https://doi.org/10.1137/20M1318389
Refined a posteriori error estimation for classical and pressure-robust Stokes finite element methods
Philip Lukas Lederer, Christian Merdon and Joachim SchöberlNumerische Mathematik 142 (3) 713 (2019)
https://doi.org/10.1007/s00211-019-01049-3
Finite elements for scalar convection-dominated equations and incompressible flow problems: a never ending story?
Volker John, Petr Knobloch and Julia NovoComputing and Visualization in Science 19 (5-6) 47 (2018)
https://doi.org/10.1007/s00791-018-0290-5
Quasi-optimality of a pressure-robust nonconforming finite element method for the Stokes-problem
A. Linke, C. Merdon, M. Neilan and F. NeumannMathematics of Computation 87 (312) 1543 (2018)
https://doi.org/10.1090/mcom/3344
The analogue of grad–div stabilization in DG methods for incompressible flows: Limiting behavior and extension to tensor-product meshes
Mine Akbas, Alexander Linke, Leo G. Rebholz and Philipp W. SchroederComputer Methods in Applied Mechanics and Engineering 341 917 (2018)
https://doi.org/10.1016/j.cma.2018.07.019
On Really Locking-Free Mixed Finite Element Methods for the Transient Incompressible Stokes Equations
Naveed Ahmed, Alexander Linke and Christian MerdonSIAM Journal on Numerical Analysis 56 (1) 185 (2018)
https://doi.org/10.1137/17M1112017
Polynomial robust stability analysis for $H$(div)-conforming finite elements for the Stokes equations
Philip L Lederer and Joachim SchöberlIMA Journal of Numerical Analysis 38 (4) 1832 (2018)
https://doi.org/10.1093/imanum/drx051
Towards computable flows and robust estimates for inf-sup stable FEM applied to the time-dependent incompressible Navier–Stokes equations
Philipp W. Schroeder, Christoph Lehrenfeld, Alexander Linke and Gert LubeSeMA Journal 75 (4) 629 (2018)
https://doi.org/10.1007/s40324-018-0157-1
Towards Pressure-Robust Mixed Methods for the Incompressible Navier–Stokes Equations
Naveed Ahmed, Alexander Linke and Christian MerdonComputational Methods in Applied Mathematics 18 (3) 353 (2018)
https://doi.org/10.1515/cmam-2017-0047
Efficient and scalable discretization of the Navier–Stokes equations with LPS modeling
Ryadh Haferssas, Pierre Jolivet and Samuele RubinoComputer Methods in Applied Mechanics and Engineering 333 371 (2018)
https://doi.org/10.1016/j.cma.2018.01.026
Divergence-free Reconstruction Operators for Pressure-Robust Stokes Discretizations with Continuous Pressure Finite Elements
Philip L. Lederer, Alexander Linke, Christian Merdon and Joachim SchöberlSIAM Journal on Numerical Analysis 55 (3) 1291 (2017)
https://doi.org/10.1137/16M1089964
Stabilised dG-FEM for incompressible natural convection flows with boundary and moving interior layers on non-adapted meshes
Philipp W. Schroeder and Gert LubeJournal of Computational Physics 335 760 (2017)
https://doi.org/10.1016/j.jcp.2017.01.055
Fluid-structure Interactions
Thomas RichterLecture Notes in Computational Science and Engineering, Fluid-structure Interactions 118 117 (2017)
https://doi.org/10.1007/978-3-319-63970-3_4
Pressure-robust analysis of divergence-free and conforming FEM for evolutionary incompressible Navier–Stokes flows
Philipp W. Schroeder and Gert LubeJournal of Numerical Mathematics 25 (4) (2017)
https://doi.org/10.1515/jnma-2016-1101
On the Divergence Constraint in Mixed Finite Element Methods for Incompressible Flows
Volker John, Alexander Linke, Christian Merdon, Michael Neilan and Leo G. RebholzSIAM Review 59 (3) 492 (2017)
https://doi.org/10.1137/15M1047696
OptimalL2velocity error estimate for a modified pressure-robust Crouzeix–Raviart Stokes element
A. Linke, C. Merdon and W. WollnerIMA Journal of Numerical Analysis 37 (1) 354 (2017)
https://doi.org/10.1093/imanum/drw019
A discontinuous skeletal method for the viscosity-dependent Stokes problem
Daniele A. Di Pietro, Alexandre Ern, Alexander Linke and Friedhelm SchieweckComputer Methods in Applied Mechanics and Engineering 306 175 (2016)
https://doi.org/10.1016/j.cma.2016.03.033
Finite Element Methods for Incompressible Flow Problems
Volker JohnSpringer Series in Computational Mathematics, Finite Element Methods for Incompressible Flow Problems 51 137 (2016)
https://doi.org/10.1007/978-3-319-45750-5_4
Pressure-robustness and discrete Helmholtz projectors in mixed finite element methods for the incompressible Navier–Stokes equations
A. Linke and C. MerdonComputer Methods in Applied Mechanics and Engineering 311 304 (2016)
https://doi.org/10.1016/j.cma.2016.08.018
Inverse modeling of thin layer flow cells for detection of solubility, transport and reaction coefficients from experimental data
C. Merdon, J. Fuhrmann, A. Linke, et al.Electrochimica Acta 211 1 (2016)
https://doi.org/10.1016/j.electacta.2016.05.101
On velocity errors due to irrotational forces in the Navier–Stokes momentum balance
A. Linke and C. MerdonJournal of Computational Physics 313 654 (2016)
https://doi.org/10.1016/j.jcp.2016.02.070
Boundary and Interior Layers, Computational and Asymptotic Methods - BAIL 2014
Gert Lube, Daniel Arndt and Helene DallmannLecture Notes in Computational Science and Engineering, Boundary and Interior Layers, Computational and Asymptotic Methods - BAIL 2014 108 147 (2015)
https://doi.org/10.1007/978-3-319-25727-3_12