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:
Carsten Carstensen
ESAIM: M2AN, 33 6 (1999) 1187-1202
Published online: 2002-08-15
This article has been cited by the following article(s):
102 articles | Pages:
Deep Ritz - Finite element methods: Neural network methods trained with finite elements
Georgios Grekas and Charalambos G. Makridakis Computer Methods in Applied Mechanics and Engineering 437 117798 (2025) https://doi.org/10.1016/j.cma.2025.117798
Vortex-Capturing Multiscale Spaces for the Ginzburg–Landau Equation
Maria Blum, Christian Döding and Patrick Henning Multiscale Modeling & Simulation 23 (1) 339 (2025) https://doi.org/10.1137/24M1664538
On a Mixed FEM and a FOSLS with 𝐻−1 Loads
Thomas Führer Computational Methods in Applied Mathematics 24 (2) 363 (2024) https://doi.org/10.1515/cmam-2022-0215
A CutFE-LOD method for the multiscale elliptic problems on complex domains
Kuokuo Zhang, Weibing Deng and Haijun Wu Journal of Computational and Applied Mathematics 445 115820 (2024) https://doi.org/10.1016/j.cam.2024.115820
Jan Papež 58 377 (2024) https://doi.org/10.1016/bs.aams.2024.04.002
Error estimates for the numerical approximation of optimal control problems with nonsmooth pointwise-integral control constraints
Eduardo Casas, Karl Kunisch and Mariano Mateos IMA Journal of Numerical Analysis 43 (3) 1485 (2023) https://doi.org/10.1093/imanum/drac027
Xiaoliang Song and Bo Yu 623 (2023) https://doi.org/10.1007/978-3-030-98661-2_129
Interpolation operator on negative Sobolev spaces
Lars Diening, Johannes Storn and Tabea Tscherpel Mathematics of Computation 92 (342) 1511 (2023) https://doi.org/10.1090/mcom/3824
Reliable Error Estimates for Optimal Control of Linear Elliptic PDEs with Random Inputs
Johannes Milz SIAM/ASA Journal on Uncertainty Quantification 11 (4) 1139 (2023) https://doi.org/10.1137/22M1503889
Song Xiaoliang and Yu Bo 1 (2022) https://doi.org/10.1007/978-3-030-03009-4_129-1
Local averaging type a posteriori error estimates for the nonlinear steady-state Poisson–Nernst–Planck equations
Ying Yang, Ruigang Shen, Mingjuan Fang and Shi Shu Journal of Computational and Applied Mathematics 404 113874 (2022) https://doi.org/10.1016/j.cam.2021.113874
A combined multiscale finite element method based on the LOD technique for the multiscale elliptic problems with singularities
Kuokuo Zhang, Weibing Deng and Haijun Wu Journal of Computational Physics 469 111540 (2022) https://doi.org/10.1016/j.jcp.2022.111540
Numerical approximation of control problems of non-monotone and non-coercive semilinear elliptic equations
Eduardo Casas, Mariano Mateos and Arnd Rösch Numerische Mathematik 149 (2) 305 (2021) https://doi.org/10.1007/s00211-021-01222-7
Quasi-Optimal Mesh Sequence Construction through Smoothed Adaptive Finite Element Methods
Ornela Mulita, Stefano Giani and Luca Heltai SIAM Journal on Scientific Computing 43 (3) A2211 (2021) https://doi.org/10.1137/19M1262097
State Error Estimates for the Numerical Approximation of Sparse Distributed Control Problems in the Absence of Tikhonov Regularization
Eduardo Casas and Mariano Mateos Vietnam Journal of Mathematics 49 (3) 713 (2021) https://doi.org/10.1007/s10013-021-00491-x
Michael Hintermüller and Tobias Keil 22 213 (2021) https://doi.org/10.1016/bs.hna.2020.10.003
Sparse Dirichlet optimal control problems
Mariano Mateos Computational Optimization and Applications 80 (1) 271 (2021) https://doi.org/10.1007/s10589-021-00290-7
A High-Order Approach to Elliptic Multiscale Problems with General Unstructured Coefficients
Roland Maier SIAM Journal on Numerical Analysis 59 (2) 1067 (2021) https://doi.org/10.1137/20M1364321
On the stability of Scott-Zhang type operators and application to multilevel preconditioning in fractional diffusion
Markus Faustmann, Jens Markus Melenk and Maryam Parvizi ESAIM: Mathematical Modelling and Numerical Analysis 55 (2) 595 (2021) https://doi.org/10.1051/m2an/2020079
Analysis of Finite Element Approximations of Stokes Equations with NonSmooth Data
Ricardo Durán, Lucia Gastaldi and Ariel Lombardi SIAM Journal on Numerical Analysis 58 (6) 3309 (2020) https://doi.org/10.1137/19M1305872
Estimates of the Deviation from Exact Solutions of Boundary Value Problems in Measures Stronger than the Energy Norm
S. I. Repin Computational Mathematics and Mathematical Physics 60 (5) 749 (2020) https://doi.org/10.1134/S0965542520050140
A Finite Element Method for Elliptic Dirichlet Boundary Control Problems
Michael Karkulik Computational Methods in Applied Mathematics 20 (4) 827 (2020) https://doi.org/10.1515/cmam-2019-0104
Efficient implementation of the localized orthogonal decomposition method
Christian Engwer, Patrick Henning, Axel Målqvist and Daniel Peterseim Computer Methods in Applied Mechanics and Engineering 350 123 (2019) https://doi.org/10.1016/j.cma.2019.02.040
The adaptive finite element method for the P-Laplace problem
D.J. Liu and Z.R. Chen Applied Numerical Mathematics (2019) https://doi.org/10.1016/j.apnum.2019.11.018
A FE-ADMM algorithm for Lavrentiev-regularized state-constrained elliptic control problem
Zixuan Chen, Xiaoliang Song, Xuping Zhang and Bo Yu ESAIM: Control, Optimisation and Calculus of Variations 25 5 (2019) https://doi.org/10.1051/cocv/2018019
Improved approximation rates for a parabolic control problem with an objective promoting directional sparsity
Eduardo Casas, Mariano Mateos and Arnd Rösch Computational Optimization and Applications 70 (1) 239 (2018) https://doi.org/10.1007/s10589-018-9979-0
An FE-Inexact Heterogeneous ADMM for Elliptic Optimal Control Problems with L1-Control Cost
Xiaoliang Song, Bo Yu, Yiyang Wang and Xuping Zhang Journal of Systems Science and Complexity 31 (6) 1659 (2018) https://doi.org/10.1007/s11424-018-7448-6
On a residual-based a posteriori error estimator for the total error
Jan Papež and Zdeněk Strakoš IMA Journal of Numerical Analysis 38 (3) 1164 (2018) https://doi.org/10.1093/imanum/drx037
Analysis of patch-test consistent atomistic-to-continuum coupling with higher-order finite elements
Andreas Dedner, Chistoph Ortner and Huan Wu ESAIM: Mathematical Modelling and Numerical Analysis 51 (6) 2263 (2017) https://doi.org/10.1051/m2an/2017013
Susanne C. Brenner and Carsten Carstensen 1 (2017) https://doi.org/10.1002/9781119176817.ecm2003
Efficient Discrete Lagrange Multipliers in three first-order finite element discretizations for the A Posteriori Error Control in an Obstacle Problem
C. Carstensen and K. Köhler SIAM Journal on Numerical Analysis 55 (1) 349 (2017) https://doi.org/10.1137/15M1033770
Adapted Numerical Methods for the Poisson Equation with $L^2$ Boundary Data in NonConvex Domains
Thomas Apel, Serge Nicaise and Johannes Pfefferer SIAM Journal on Numerical Analysis 55 (4) 1937 (2017) https://doi.org/10.1137/16M1062077
Thomas Apel and Jens M. Melenk 1 (2017) https://doi.org/10.1002/9781119176817.ecm2002m
Transport Processes at Fluidic Interfaces
Michael Hintermüller, Michael Hinze, Christian Kahle and Tobias Keil Advances in Mathematical Fluid Mechanics, Transport Processes at Fluidic Interfaces 305 (2017) https://doi.org/10.1007/978-3-319-56602-3_13
Atomistic/Continuum Blending with Ghost Force Correction
Christoph Ortner and Lei Zhang SIAM Journal on Scientific Computing 38 (1) A346 (2016) https://doi.org/10.1137/15M1020241
Building Bridges: Connections and Challenges in Modern Approaches to Numerical Partial Differential Equations
Daniel Peterseim Lecture Notes in Computational Science and Engineering, Building Bridges: Connections and Challenges in Modern Approaches to Numerical Partial Differential Equations 114 343 (2016) https://doi.org/10.1007/978-3-319-41640-3_11
Analysis of blended atomistic/continuum hybrid methods
Xingjie Helen Li, Christoph Ortner, Alexander V. Shapeev and Brian Van Koten Numerische Mathematik 134 (2) 275 (2016) https://doi.org/10.1007/s00211-015-0772-z
Numerical Approximation of Partial Differential Equations
Sören Bartels Texts in Applied Mathematics, Numerical Approximation of Partial Differential Equations 64 155 (2016) https://doi.org/10.1007/978-3-319-32354-1_4
Robust Numerical Upscaling of Elliptic Multiscale Problems at High Contrast
Daniel Peterseim and Robert Scheichl Computational Methods in Applied Mathematics 16 (4) 579 (2016) https://doi.org/10.1515/cmam-2016-0022
Justification of the saturation assumption
C. Carstensen, D. Gallistl and J. Gedicke Numerische Mathematik 134 (1) 1 (2016) https://doi.org/10.1007/s00211-015-0769-7
Discretization of the Poisson equation with non-smooth data and emphasis on non-convex domains
Thomas Apel, Serge Nicaise and Johannes Pfefferer Numerical Methods for Partial Differential Equations 32 (5) 1433 (2016) https://doi.org/10.1002/num.22057
A stable and linear time discretization for a thermodynamically consistent model for two-phase incompressible flow
Harald Garcke, Michael Hinze and Christian Kahle Applied Numerical Mathematics 99 151 (2016) https://doi.org/10.1016/j.apnum.2015.09.002
Numerical Approximation of Phase Field Based Shape and Topology Optimization for Fluids
Harald Garcke, Claudia Hecht, Michael Hinze and Christian Kahle SIAM Journal on Scientific Computing 37 (4) A1846 (2015) https://doi.org/10.1137/140969269
On multiscale methods in Petrov–Galerkin formulation
Daniel Elfverson, Victor Ginting and Patrick Henning Numerische Mathematik 131 (4) 643 (2015) https://doi.org/10.1007/s00211-015-0703-z
A reduced basis localized orthogonal decomposition
Assyr Abdulle and Patrick Henning Journal of Computational Physics 295 379 (2015) https://doi.org/10.1016/j.jcp.2015.04.016
Local high-order regularization and applications to hp-methods
M. Karkulik and J.M. Melenk Computers & Mathematics with Applications 70 (7) 1606 (2015) https://doi.org/10.1016/j.camwa.2015.06.026
Patrick Henning, Philipp Morgenstern and Daniel Peterseim 100 185 (2015) https://doi.org/10.1007/978-3-319-06898-5_10
Olli Mali, Pekka Neittaanmäki and Sergey Repin 32 7 (2014) https://doi.org/10.1007/978-94-007-7581-7_2
Localization of elliptic multiscale problems
Axel Målqvist and Daniel Peterseim Mathematics of Computation 83 (290) 2583 (2014) https://doi.org/10.1090/S0025-5718-2014-02868-8
Immanuel Anjam, Olli Mali, Pekka Neittaanmäki and Sergey Repin 34 1 (2014) https://doi.org/10.1007/978-94-017-9054-3_1
Two-Level Discretization Techniques for Ground State Computations of Bose-Einstein Condensates
Patrick Henning, Axel Målqvist and Daniel Peterseim SIAM Journal on Numerical Analysis 52 (4) 1525 (2014) https://doi.org/10.1137/130921520
Localized Orthogonal Decomposition Techniques for Boundary Value Problems
Patrick Henning and Axel Målqvist SIAM Journal on Scientific Computing 36 (4) A1609 (2014) https://doi.org/10.1137/130933198
New Error Estimates of Nonconforming Finite Element Methods for the Poisson Problem with Low Regularity Solution
Youai Li Advances in Applied Mathematics and Mechanics 6 (2) 179 (2014) https://doi.org/10.4208/aamm.12-m12126
A localized orthogonal decomposition method for semi-linear elliptic problems
Patrick Henning, Axel Målqvist and Daniel Peterseim ESAIM: Mathematical Modelling and Numerical Analysis 48 (5) 1331 (2014) https://doi.org/10.1051/m2an/2013141
A posteriori error estimator competition for conforming obstacle problems
C. Carstensen and C. Merdon Numerical Methods for Partial Differential Equations 29 (2) 667 (2013) https://doi.org/10.1002/num.21728
Another view for a posteriori error estimates for variational inequalities of the second kind
Fei Wang and Weimin Han Applied Numerical Mathematics 72 225 (2013) https://doi.org/10.1016/j.apnum.2013.07.002
AN ADAPTIVE FINITE ELEMENT APPROXIMATION OF A GENERALIZED AMBROSIO–TORTORELLI FUNCTIONAL
SIOBHAN BURKE, CHRISTOPH ORTNER and ENDRE SÜLI Mathematical Models and Methods in Applied Sciences 23 (09) 1663 (2013) https://doi.org/10.1142/S021820251350019X
A Posteriori Error Estimates and Adaptive Mesh Refinement for the Coupling of the Finite Volume Method and the Boundary Element Method
Christoph Erath SIAM Journal on Numerical Analysis 51 (3) 1777 (2013) https://doi.org/10.1137/110854771
Stability of semilinear elliptic optimal control problems with pointwise state constraints
M. Hinze and C. Meyer Computational Optimization and Applications 52 (1) 87 (2012) https://doi.org/10.1007/s10589-011-9410-6
Large-Scale Scientific Computing
Eduardo Casas, Roland Herzog and Gerd Wachsmuth Lecture Notes in Computer Science, Large-Scale Scientific Computing 7116 16 (2012) https://doi.org/10.1007/978-3-642-29843-1_2
Approximation of sparse controls in semilinear equations by piecewise linear functions
Eduardo Casas, Roland Herzog and Gerd Wachsmuth Numerische Mathematik 122 (4) 645 (2012) https://doi.org/10.1007/s00211-012-0475-7
Finite Element Analysis of an Optimal Control Problem in the Coefficients of Time-Harmonic Eddy Current Equations
Irwin Yousept Journal of Optimization Theory and Applications 154 (3) 879 (2012) https://doi.org/10.1007/s10957-012-0040-7
Convergence and regularization results for optimal control problems with sparsity functional
Gerd Wachsmuth and Daniel Wachsmuth ESAIM: Control, Optimisation and Calculus of Variations 17 (3) 858 (2011) https://doi.org/10.1051/cocv/2010027
A Priori and a Posteriori Error Analysis of the Discontinuous Galerkin Methods for Reissner-Mindlin Plates
Jun Hu and Yunqing Huang Advances in Applied Mathematics and Mechanics 3 (6) 649 (2011) https://doi.org/10.4208/aamm.11-m1111
Convergence and quasi-optimality of adaptive nonconforming finite element methods for some nonsymmetric and indefinite problems
Huangxin Chen, Xuejun Xu and Ronald H. W. Hoppe Numerische Mathematik 116 (3) 383 (2010) https://doi.org/10.1007/s00211-010-0307-6
A Priori Error Analysis for Linear Quadratic Elliptic Neumann Boundary Control Problems with Control and State Constraints
K. Krumbiegel, C. Meyer and A. R�sch SIAM Journal on Control and Optimization 48 (8) 5108 (2010) https://doi.org/10.1137/090746148
A Posteriori Error Estimates for Finite Element Approximation of Unsteady Incompressible Stochastic Navier–Stokes Equations
Xiaoyuan Yang, Yuanyuan Duan and Yuhua Guo SIAM Journal on Numerical Analysis 48 (4) 1579 (2010) https://doi.org/10.1137/080732080
Convergence and quasi-optimal complexity of a simple adaptive finite element method
Roland Becker and Shipeng Mao ESAIM: Mathematical Modelling and Numerical Analysis 43 (6) 1203 (2009) https://doi.org/10.1051/m2an/2009036
A posteriori error analysis of nonconforming methods for the eigenvalue problem
Youai Li Journal of Systems Science and Complexity 22 (3) 495 (2009) https://doi.org/10.1007/s11424-009-9181-7
Convergence of adaptive finite element methods in computational mechanics
Carsten Carstensen Applied Numerical Mathematics 59 (9) 2119 (2009) https://doi.org/10.1016/j.apnum.2008.12.006
A new a posteriori error estimate for the Morley element
Jun Hu and Zhongci Shi Numerische Mathematik 112 (1) 25 (2009) https://doi.org/10.1007/s00211-008-0205-3
ECCOMAS Multidisciplinary Jubilee Symposium
P. Neittaanmäki and S. Repin ECCOMAS Multidisciplinary Jubilee Symposium 14 203 (2009) https://doi.org/10.1007/978-1-4020-9231-2_14
Mixed Finite Element Technologies
C. Carstensen CISM International Centre for Mechanical Sciences, Mixed Finite Element Technologies 509 1 (2009) https://doi.org/10.1007/978-3-211-99094-0_1
Viorel Bostan and Weimin Han 17 25 (2009) https://doi.org/10.1007/978-0-387-75714-8_3
A unifying theory of a posteriori error control for nonconforming finite element methods
C. Carstensen and Jun Hu Numerische Mathematik 107 (3) 473 (2007) https://doi.org/10.1007/s00211-007-0068-z
Framework for the A Posteriori Error Analysis of Nonconforming Finite Elements
Carsten Carstensen, Jun Hu and Antonio Orlando SIAM Journal on Numerical Analysis 45 (1) 68 (2007) https://doi.org/10.1137/050628854
Convergence analysis of an adaptive nonconforming finite element method
Carsten Carstensen and Ronald H.W. Hoppe Numerische Mathematik 103 (2) 251 (2006) https://doi.org/10.1007/s00211-005-0658-6
Partial Differential Equations and Functional Analysis
Carsten Carstensen Partial Differential Equations and Functional Analysis 27 (2006) https://doi.org/10.1007/3-7643-7601-5_2
A posteriori FE error control for p-Laplacian by gradient recovery in quasi-norm
Carsten Carstensen, W. Liu and N. Yan Mathematics of Computation 75 (256) 1599 (2006) https://doi.org/10.1090/S0025-5718-06-01819-9
A convergent adaptive finite element method for the primal problem of elastoplasticity
Carsten Carstensen, Antonio Orlando and Jan Valdman International Journal for Numerical Methods in Engineering 67 (13) 1851 (2006) https://doi.org/10.1002/nme.1686
Adaptive finite element algorithms for eigenvalue problems based on local averaging type a posteriori error estimates
Dong Mao, Lihua Shen and Aihui Zhou Advances in Computational Mathematics 25 (1-3) 135 (2006) https://doi.org/10.1007/s10444-004-7617-0
Residual-based a posteriori error estimate for a mixed Reißner-Mindlin plate finite element method
Carsten Carstensen and Joachim Schöberl Numerische Mathematik 103 (2) 225 (2006) https://doi.org/10.1007/s00211-005-0669-3
Local averaging based a posteriori finite element error control for quasilinear elliptic problems with application to electrical potential computation
Ying Yang and Aihui Zhou Computer Methods in Applied Mechanics and Engineering 196 (1-3) 452 (2006) https://doi.org/10.1016/j.cma.2006.05.008
A Posteriori Error Estimates for Finite Element Approximation of Parabolic p-Laplacian
Carsten Carstensen, Wenbin Liu and Ningning Yan SIAM Journal on Numerical Analysis 43 (6) 2294 (2006) https://doi.org/10.1137/040611008
A posteriori error analysis for time-dependent Ginzburg-Landau type equations
S�ren Bartels Numerische Mathematik 99 (4) 557 (2005) https://doi.org/10.1007/s00211-004-0560-7
Thomas Apel (2004) https://doi.org/10.1002/0470091355.ecm002m
Susanne C. Brenner and Carsten Carstensen (2004) https://doi.org/10.1002/0470091355.ecm003
Averaging techniques yield reliable a posteriori finite element error control for obstacle problems
S. Bartels and C. Carstensen Numerische Mathematik 99 (2) 225 (2004) https://doi.org/10.1007/s00211-004-0553-6
Inhomogeneous Dirichlet conditions in a priori and a posteriori finite element error analysis
S. Bartels, C. Carstensen and G. Dolzmann Numerische Mathematik 99 (1) 1 (2004) https://doi.org/10.1007/s00211-004-0548-3
Some remarks on the history and future of averaging techniques in a posteriori finite element error analysis
C. Carstensen ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik 84 (1) 3 (2004) https://doi.org/10.1002/zamm.200410101
On the Convergence of Adaptive Finite Element Methods
Carsten Carstensen PAMM 4 (1) 27 (2004) https://doi.org/10.1002/pamm.200410007
Adaptive Approximation of Young Measure Solutions in Scalar Nonconvex Variational Problems
So?ren Bartels SIAM Journal on Numerical Analysis 42 (2) 505 (2004) https://doi.org/10.1137/S0036142902404091
Reliable Methods for Computer Simulation - Error Control and A Posteriori Estimates
Studies in Mathematics and Its Applications, Reliable Methods for Computer Simulation - Error Control and A Posteriori Estimates 33 281 (2004) https://doi.org/10.1016/S0168-2024(04)80010-9
A Posteriori Finite Element Error Control for the P-Laplace Problem
Carsten Carstensen and R. Klose SIAM Journal on Scientific Computing 25 (3) 792 (2003) https://doi.org/10.1137/S1064827502416617
A Posteriori Error Estimators of Gradient Recovery Type for Fem of a Model Optimal Control Problem
Ningning Yan Advances in Computational Mathematics 19 (1-3) 323 (2003) https://doi.org/10.1023/A:1022800401298
Averaging techniques for reliable a posteriori FE-error control in elastoplasticity with hardening
Carsten Carstensen and Jochen Alberty Computer Methods in Applied Mechanics and Engineering 192 (11-12) 1435 (2003) https://doi.org/10.1016/S0045-7825(02)00648-5
Error estimates and adaptive finite element methods
Jaroslav Mackerle Engineering Computations 18 (5/6) 802 (2001) https://doi.org/10.1108/EUM0000000005788
Averaging technique for a posteriori error control in elasticity. Part III: Locking-free nonconforming FEM
Carsten Carstensen and Stefan A. Funken Computer Methods in Applied Mechanics and Engineering 191 (8-10) 861 (2001) https://doi.org/10.1016/S0045-7825(01)00202-X
An experimental survey of a posteriori Courant finite element error control for the Poisson equation
Carsten Carstensen, Sören Bartels and Roland Klose Advances in Computational Mathematics 15 (1-4) 79 (2001) https://doi.org/10.1023/A:1014269318616
Averaging technique for FE – a posteriori error control in elasticity. Part II: λ-independent estimates
Carsten Carstensen and Stefan A. Funken Computer Methods in Applied Mechanics and Engineering 190 (35-36) 4663 (2001) https://doi.org/10.1016/S0045-7825(00)00338-8
Pages:
1 to 100 of 102 articles