EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues ESAIM: M2AN, 35 6 (2001) 1055-1078 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:

Mean square temporal error estimates for the two-dimensional stochastic Navier–Stokes equations with transport noise

D Breit, T C Moyo, A Prohl and J Wichmann
IMA Journal of Numerical Analysis (2025)
https://doi.org/10.1093/imanum/draf042

Total Variation Error Bounds for the Approximation of the Invariant Distribution of Parabolic Semilinear SPDEs Using the Standard Euler Scheme

Charles-Edouard Bréhier
Potential Analysis 62 (1) 101 (2025)
https://doi.org/10.1007/s11118-024-10132-w

Rate of convergence of a semi-implicit time euler scheme for a 2D bénard–boussinesq model

Hakima Bessaih and Annie Millet
Stochastics and Partial Differential Equations: Analysis and Computations (2025)
https://doi.org/10.1007/s40072-024-00347-8

Analysis of a Modified Regularity-Preserving Euler Scheme for Parabolic Semilinear SPDEs: Total Variation Error Bounds for the Numerical Approximation of the Invariant Distribution

Charles-Edouard Bréhier
Foundations of Computational Mathematics 25 (2) 511 (2025)
https://doi.org/10.1007/s10208-024-09644-z

Long-term accuracy of numerical approximations of SPDEs with the stochastic Navier–Stokes equations as a paradigm

Nathan E Glatt-Holtz and Cecilia F Mondaini
IMA Journal of Numerical Analysis 45 (3) 1648 (2025)
https://doi.org/10.1093/imanum/drae043

Analysis of a positivity-preserving splitting scheme for some semilinear stochastic heat equations

Charles-Edouard Bréhier, David Cohen and Johan Ulander
ESAIM: Mathematical Modelling and Numerical Analysis 58 (4) 1317 (2024)
https://doi.org/10.1051/m2an/2024032

Weak error analysis for the stochastic Allen–Cahn equation

Dominic Breit and Andreas Prohl
Stochastics and Partial Differential Equations: Analysis and Computations 12 (4) 2181 (2024)
https://doi.org/10.1007/s40072-024-00326-z

Total Variation Error Bounds for the Accelerated Exponential Euler Scheme Approximation of Parabolic Semilinear SPDEs

Charles-Edouard Bréhier
SIAM Journal on Numerical Analysis 62 (3) 1171 (2024)
https://doi.org/10.1137/22M152596X

Error Analysis for 2D Stochastic Navier–Stokes Equations in Bounded Domains with Dirichlet Data

Dominic Breit and Andreas Prohl
Foundations of Computational Mathematics 24 (5) 1643 (2024)
https://doi.org/10.1007/s10208-023-09621-y

Higher order time discretization method for a class of semilinear stochastic partial differential equations with multiplicative noise

Yukun Li, Liet Vo and Guanqian Wang
Journal of Computational and Applied Mathematics 437 115442 (2024)
https://doi.org/10.1016/j.cam.2023.115442

Positivity and dynamics preserving discretization schemes for nonlinear evolution equations

Priyanka Saha, Nandadulal Bairagi and Gaston N'Guerekata
Malaya Journal of Matematik 12 (01) 1 (2024)
https://doi.org/10.26637/mjm1201/001

Splitting schemes for FitzHugh–Nagumo stochastic partial differential equations

Charles-Edouard Bréhier, David Cohen and Giuseppe Giordano
Discrete and Continuous Dynamical Systems - B (2023)
https://doi.org/10.3934/dcdsb.2023094

Some approximation results for mild solutions of stochastic fractional order evolution equations driven by Gaussian noise

K. Fahim, E. Hausenblas and M. Kovács
Stochastics and Partial Differential Equations: Analysis and Computations 11 (3) 1044 (2023)
https://doi.org/10.1007/s40072-022-00250-0

A splitting semi-implicit Euler method for stochastic incompressible Euler equations on 𝕋2

Jialin Hong, Derui Sheng and Tau Zhou
IMA Journal of Numerical Analysis 43 (5) 2748 (2023)
https://doi.org/10.1093/imanum/drac054

Numerical approximation of nonlinear SPDE’s

Martin Ondreját, Andreas Prohl and Noel J. Walkington
Stochastics and Partial Differential Equations: Analysis and Computations 11 (4) 1553 (2023)
https://doi.org/10.1007/s40072-022-00271-9

Optimal Rate of Convergence for Approximations of SPDEs with Nonregular Drift

Oleg Butkovsky, Konstantinos Dareiotis and Máté Gerencsér
SIAM Journal on Numerical Analysis 61 (2) 1103 (2023)
https://doi.org/10.1137/21M1454213

Approximated exponential integrators for the stochastic Manakov equation

André Berg, David Cohen and Guillaume Dujardin
Journal of Computational Dynamics (2023)
https://doi.org/10.3934/jcd.2023002

Convergence analysis of explicit stabilized integrators for parabolic semilinear stochastic PDEs

Assyr Abdulle, Charles-Edouard Bréhier and Gilles Vilmart
IMA Journal of Numerical Analysis 43 (1) 258 (2023)
https://doi.org/10.1093/imanum/drab090

Numerical conservation issues for the stochastic Korteweg–de Vries equation

Raffaele D’Ambrosio and Stefano Di Giovacchino
Journal of Computational and Applied Mathematics 424 114967 (2023)
https://doi.org/10.1016/j.cam.2022.114967

Strong $$L^2$$ convergence of time Euler schemes for stochastic 3D Brinkman–Forchheimer–Navier–Stokes equations

Hakima Bessaih and Annie Millet
Stochastics and Partial Differential Equations: Analysis and Computations 10 (3) 1005 (2022)
https://doi.org/10.1007/s40072-022-00255-9

Space-time Euler discretization schemes for the stochastic 2D Navier–Stokes equations

Hakima Bessaih and Annie Millet
Stochastics and Partial Differential Equations: Analysis and Computations 10 (4) 1515 (2022)
https://doi.org/10.1007/s40072-021-00217-7

An efficient numerical approach for stochastic evolution PDEs driven by random diffusion coefficients and multiplicative noise

Xiao Qi, Mejdi Azaiez, Can Huang and Chuanju Xu
AIMS Mathematics 7 (12) 20684 (2022)
https://doi.org/10.3934/math.20221134

Speed of Convergence of Time Euler Schemes for a Stochastic 2D Boussinesq Model

Hakima Bessaih and Annie Millet
Mathematics 10 (22) 4246 (2022)
https://doi.org/10.3390/math10224246

Analysis of Fully Discrete Mixed Finite Element Methods for Time-dependent Stochastic Stokes Equations with Multiplicative Noise

Xiaobing Feng and Hailong Qiu
Journal of Scientific Computing 88 (2) (2021)
https://doi.org/10.1007/s10915-021-01546-4

Convergence in Hölder norms with applications to Monte Carlo methods in infinite dimensions

Sonja Cox, Martin Hutzenthaler, Arnulf Jentzen, Jan van Neerven and Timo Welti
IMA Journal of Numerical Analysis 41 (1) 493 (2021)
https://doi.org/10.1093/imanum/drz063

Fractional stochastic Burgers‐type equation in Hölder space—Wellposedness and approximations

Zineb Arab and Latifa Debbi
Mathematical Methods in the Applied Sciences 44 (1) 705 (2021)
https://doi.org/10.1002/mma.6776

Spectral collocation method for stochastic partial differential equations with fractional Brownian motion

Mahdieh Arezoomandan and Ali R. Soheili
Journal of Computational and Applied Mathematics 389 113369 (2021)
https://doi.org/10.1016/j.cam.2020.113369

Convergence rates for the numerical approximation of the 2D stochastic Navier–Stokes equations

Dominic Breit and Alan Dodgson
Numerische Mathematik 147 (3) 553 (2021)
https://doi.org/10.1007/s00211-021-01181-z

Geometric Partial Differential Equations - Part I

Qiang Du and Xiaobing Feng
Handbook of Numerical Analysis, Geometric Partial Differential Equations - Part I 21 425 (2020)
https://doi.org/10.1016/bs.hna.2019.05.001

On a perturbation theory and on strong convergence rates for stochastic ordinary and partial differential equations with nonglobally monotone coefficients

Martin Hutzenthaler and Arnulf Jentzen
The Annals of Probability 48 (1) (2020)
https://doi.org/10.1214/19-AOP1345

An efficient explicit full-discrete scheme for strong approximation of stochastic Allen–Cahn equation

Xiaojie Wang
Stochastic Processes and their Applications 130 (10) 6271 (2020)
https://doi.org/10.1016/j.spa.2020.05.011

Influence of the regularity of the test functions for weak convergence in numerical discretization of SPDEs

Charles-Edouard Bréhier
Journal of Complexity 56 101424 (2020)
https://doi.org/10.1016/j.jco.2019.101424

Strong convergence rates for an explicit numerical approximation method for stochastic evolution equations with non-globally Lipschitz continuous nonlinearities

Primož Pušnik and Arnulf Jentzen
IMA Journal of Numerical Analysis 40 (2) 1005 (2020)
https://doi.org/10.1093/imanum/drz009

A fully discrete approximation of the one-dimensional stochastic heat equation

Rikard Anton, David Cohen and Lluis Quer-Sardanyons
IMA Journal of Numerical Analysis 40 (1) 247 (2020)
https://doi.org/10.1093/imanum/dry060

Strong convergence of a stochastic Rosenbrock-type scheme for the finite element discretization of semilinear SPDEs driven by multiplicative and additive noise

Jean Daniel Mukam and Antoine Tambue
Stochastic Processes and their Applications 130 (8) 4968 (2020)
https://doi.org/10.1016/j.spa.2020.02.008

Strong convergence of the linear implicit Euler method for the finite element discretization of semilinear SPDEs driven by multiplicative or additive noise

Antoine Tambue and Jean Daniel Mukam
Applied Mathematics and Computation 346 23 (2019)
https://doi.org/10.1016/j.amc.2018.09.073

Strong $L^2$ convergence of time numerical schemes for the stochastic two-dimensional Navier–Stokes equations

Annie Millet and Hakima Bessaih
IMA Journal of Numerical Analysis 39 (4) 2135 (2019)
https://doi.org/10.1093/imanum/dry058

Time-discretization of stochastic 2-D Navier–Stokes equations with a penalty-projection method

Erika Hausenblas and Tsiry A. Randrianasolo
Numerische Mathematik 143 (2) 339 (2019)
https://doi.org/10.1007/s00211-019-01057-3

Strong convergence of the linear implicit Euler method for the finite element discretization of semilinear non-autonomous SPDEs driven by multiplicative or additive noise

Jean Daniel Mukam and Antoine Tambue
Applied Numerical Mathematics (2019)
https://doi.org/10.1016/j.apnum.2019.08.009

Strong convergence rates of semidiscrete splitting approximations for the stochastic Allen–Cahn equation

Charles-Edouard Bréhier, Jianbo Cui and Jialin Hong
IMA Journal of Numerical Analysis 39 (4) 2096 (2019)
https://doi.org/10.1093/imanum/dry052

Error estimates of finite element methods for fractional stochastic Navier–Stokes equations

Xiaocui Li and Xiaoyuan Yang
Journal of Inequalities and Applications 2018 (1) (2018)
https://doi.org/10.1186/s13660-018-1880-y

Strong Convergence of a Fully Discrete Finite Element Approximation of the Stochastic Cahn--Hilliard Equation

Daisuke Furihata, Mihály Kovács, Stig Larsson and Fredrik Lindgren
SIAM Journal on Numerical Analysis 56 (2) 708 (2018)
https://doi.org/10.1137/17M1121627

Optimal Strong Rates of Convergence for a Space-Time Discretization of the Stochastic Allen–Cahn Equation with Multiplicative Noise

Ananta K. Majee and Andreas Prohl
Computational Methods in Applied Mathematics 18 (2) 297 (2018)
https://doi.org/10.1515/cmam-2017-0023

Implicit Euler method for numerical solution of nonlinear stochastic partial differential equations with multiplicative trace class noise

Minoo Kamrani, S. Mohammad Hosseini and Erika Hausenblas
Mathematical Methods in the Applied Sciences 41 (13) 4986 (2018)
https://doi.org/10.1002/mma.4946

Strong Convergence Analysis of the Stochastic Exponential Rosenbrock Scheme for the Finite Element Discretization of Semilinear SPDEs Driven by Multiplicative and Additive Noise

Jean Daniel Mukam and Antoine Tambue
Journal of Scientific Computing 74 (2) 937 (2018)
https://doi.org/10.1007/s10915-017-0475-y

Numerical Solution of Stochastic Generalized Fractional Diffusion Equation by Finite Difference Method

Amaneh Sepahvandzadeh, Bahman Ghazanfari and Nader Asadian
Mathematical and Computational Applications 23 (4) 53 (2018)
https://doi.org/10.3390/mca23040053

Crank--Nicolson Finite Element Approximations for a Linear Stochastic Fourth Order Equation with Additive Space-Time White Noise

Georgios E. Zouraris
SIAM Journal on Numerical Analysis 56 (2) 838 (2018)
https://doi.org/10.1137/15M1053098

Numerical approximation of stochastic evolution equations: Convergence in scale of Hilbert spaces

Hakima Bessaih, Erika Hausenblas, Tsiry Avisoa Randrianasolo and Paul André Razafimandimby
Journal of Computational and Applied Mathematics 343 250 (2018)
https://doi.org/10.1016/j.cam.2018.04.067

Numerical Methods for Stochastic Partial Differential Equations with White Noise

Zhongqiang Zhang and George Em Karniadakis
Applied Mathematical Sciences, Numerical Methods for Stochastic Partial Differential Equations with White Noise 196 53 (2017)
https://doi.org/10.1007/978-3-319-57511-7_3

Convergence of the spectral Galerkin method for the stochastic reaction–diffusion–advection equation

Li Yang and Yanzhi Zhang
Journal of Mathematical Analysis and Applications 446 (2) 1230 (2017)
https://doi.org/10.1016/j.jmaa.2016.09.028

Difference Approximation of Stochastic Elastic Equation Driven by Infinite Dimensional Noise

Yinghan Zhang, Xiaoyuan Yang and Ruisheng Qi
Numerical Mathematics: Theory, Methods and Applications 9 (1) 123 (2016)
https://doi.org/10.4208/nmtma.2015.y14002

On the Convergence Analysis of the Inexact Linearly Implicit Euler Scheme for a Class of Stochastic Partial Differential Equations

P. A. Cioica, S. Dahlke, N. Döhring, et al.
Potential Analysis 44 (3) 473 (2016)
https://doi.org/10.1007/s11118-015-9510-5

Numerical solution of stochastic partial differential equations using a collocation method

Minoo Kamrani
ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik 96 (1) 106 (2016)
https://doi.org/10.1002/zamm.201400080

Strong convergence rates of the linear implicit Euler method for the finite element discretization of SPDEs with additive noise

Xiaojie Wang
IMA Journal of Numerical Analysis drw016 (2016)
https://doi.org/10.1093/imanum/drw016

On the Rate of Convergence of the 2-D Stochastic Leray- $$\alpha $$ α Model to the 2-D Stochastic Navier–Stokes Equations with Multiplicative Noise

Hakima Bessaih and Paul André Razafimandimby
Applied Mathematics & Optimization 74 (1) 1 (2016)
https://doi.org/10.1007/s00245-015-9303-7

On the Backward Euler Approximation of the Stochastic Allen-Cahn Equation

Mihály Kovács, Stig Larsson and Fredrik Lindgren
Journal of Applied Probability 52 (2) 323 (2015)
https://doi.org/10.1239/jap/1437658601

On the Backward Euler Approximation of the Stochastic Allen-Cahn Equation

Mihály Kovács, Stig Larsson and Fredrik Lindgren
Journal of Applied Probability 52 (02) 323 (2015)
https://doi.org/10.1017/S0021900200012493

A fully discrete approximation of the one-dimensional stochastic wave equation

David Cohen and Lluís Quer-Sardanyons
IMA Journal of Numerical Analysis drv006 (2015)
https://doi.org/10.1093/imanum/drv006

Existence, uniqueness and regularity for a class of semilinear stochastic Volterra equations with multiplicative noise

Boris Baeumer, Matthias Geissert and Mihály Kovács
Journal of Differential Equations 258 (2) 535 (2015)
https://doi.org/10.1016/j.jde.2014.09.020

Splitting up method for the 2D stochastic Navier–Stokes equations

H. Bessaih, Z. Brzeźniak and A. Millet
Stochastic Partial Differential Equations: Analysis and Computations 2 (4) 433 (2014)
https://doi.org/10.1007/s40072-014-0041-7

Probability and Pathwise Order of Convergence of a Semidiscrete Scheme for the Stochastic Manakov Equation

Maxime Gazeau
SIAM Journal on Numerical Analysis 52 (1) 533 (2014)
https://doi.org/10.1137/13090924X

Mean Square Convergent Finite Difference Scheme for Stochastic Parabolic PDEs

W. W. Mohammed, M. A. Sohaly, A. H. El-Bassiouny and K. A. Elnagar
American Journal of Computational Mathematics 04 (04) 280 (2014)
https://doi.org/10.4236/ajcm.2014.44024

A Hybrid Sparse-Grid Approach for Nonlinear Filtering Problems Based on Adaptive-Domain of the Zakai Equation Approximations

Feng Bao, Yanzhao Cao, Clayton Webster and Guannan Zhang
SIAM/ASA Journal on Uncertainty Quantification 2 (1) 784 (2014)
https://doi.org/10.1137/140952910

A Simplified Milstein Scheme for SPDEs with Multiplicative Noise

B. Ghayebi and S. M. Hosseini
Abstract and Applied Analysis 2014 1 (2014)
https://doi.org/10.1155/2014/140849

Finite element approximations for a linear fourth-order parabolic SPDE in two and three space dimensions with additive space–time white noise

Georgios T. Kossioris and Georgios E. Zouraris
Applied Numerical Mathematics 67 243 (2013)
https://doi.org/10.1016/j.apnum.2012.01.003

Pathwise Hölder convergence of the implicit-linear Euler scheme for semi-linear SPDEs with multiplicative noise

Sonja Cox and Jan van Neerven
Numerische Mathematik 125 (2) 259 (2013)
https://doi.org/10.1007/s00211-013-0538-4

Weak convergence analysis of the linear implicit Euler method for semilinear stochastic partial differential equations with additive noise

Xiaojie Wang and Siqing Gan
Journal of Mathematical Analysis and Applications 398 (1) 151 (2013)
https://doi.org/10.1016/j.jmaa.2012.08.038

Monte Carlo and Quasi-Monte Carlo Methods 2012

Mihály Kovács, Stig Larsson and Karsten Urban
Springer Proceedings in Mathematics & Statistics, Monte Carlo and Quasi-Monte Carlo Methods 2012 65 481 (2013)
https://doi.org/10.1007/978-3-642-41095-6_24

Order of Convergence of Splitting Schemes for Both Deterministic and Stochastic Nonlinear Schrödinger Equations

Jie Liu
SIAM Journal on Numerical Analysis 51 (4) 1911 (2013)
https://doi.org/10.1137/12088416X

Finite element approximations for a linear Cahn-Hilliard-Cook equation driven by the space derivative of a space-time white noise

Georgios T. Kossioris and Georgios E. Zouraris
Discrete & Continuous Dynamical Systems - B 18 (7) 1845 (2013)
https://doi.org/10.3934/dcdsb.2013.18.1845

Domain decomposition strategies for the stochastic heat equation

Erich Carelli, Alexander Müller and Andreas Prohl
International Journal of Computer Mathematics 89 (18) 2517 (2012)
https://doi.org/10.1080/00207160.2012.720977

Pathwise space approximations of semi-linear parabolic SPDEs with multiplicative noise

Sonja Cox and Erika Hausenblas
International Journal of Computer Mathematics 89 (18) 2460 (2012)
https://doi.org/10.1080/00207160.2012.737460

Stochastic Analysis and Related Topics

Zdzisław Brzeźniak and Annie Millet
Springer Proceedings in Mathematics & Statistics, Stochastic Analysis and Related Topics 22 57 (2012)
https://doi.org/10.1007/978-3-642-29982-7_3

Optimal regularity for semilinear stochastic partial differential equations with multiplicative noise

Raphael Kruse and Stig Larsson
Electronic Journal of Probability 17 (none) (2012)
https://doi.org/10.1214/EJP.v17-2240

Rates of Convergence for Discretizations of the Stochastic Incompressible Navier--Stokes Equations

Erich Carelli and Andreas Prohl
SIAM Journal on Numerical Analysis 50 (5) 2467 (2012)
https://doi.org/10.1137/110845008

Numerical methods for stochastic partial differential equations with multiple scales

A. Abdulle and G.A. Pavliotis
Journal of Computational Physics 231 (6) 2482 (2012)
https://doi.org/10.1016/j.jcp.2011.11.039

Higher Order Pathwise Numerical Approximations of SPDEs with Additive Noise

Arnulf Jentzen
SIAM Journal on Numerical Analysis 49 (2) 642 (2011)
https://doi.org/10.1137/080740714

Asymptotics for a generalized Cahn-Hilliard equation with forcing terms

Dimitra Antonopoulou, Georgia Karali and Georgios T. Kossioris
Discrete & Continuous Dynamical Systems - A 30 (4) 1037 (2011)
https://doi.org/10.3934/dcds.2011.30.1037

Fully-discrete finite element approximations for a fourth-order linear stochastic parabolic equation with additive space-time white noise

Georgios T. Kossioris and Georgios E. Zouraris
ESAIM: Mathematical Modelling and Numerical Analysis 44 (2) 289 (2010)
https://doi.org/10.1051/m2an/2010003

Finite Element Approximation of Stochastic Partial Differential Equations driven by Poisson Random Measures of Jump Type

Erika Hausenblas
SIAM Journal on Numerical Analysis 46 (1) 437 (2008)
https://doi.org/10.1137/050654141

Discretization and Simulation of the Zakai Equation

Emmanuel Gobet, Gilles Page?s, Huye^n Pham and Jacques Printems
SIAM Journal on Numerical Analysis 44 (6) 2505 (2006)
https://doi.org/10.1137/050623140

A numerical approximation of parabolic stochastic partial differential equations driven by a Poisson random measure

Erika Hausenblas and Iuliana Marchis
BIT Numerical Mathematics 46 (4) 773 (2006)
https://doi.org/10.1007/s10543-006-0099-3

On implicit and explicit discretization schemes for parabolic SPDEs in any dimension

Annie Millet and Pierre-Luc Morien
Stochastic Processes and their Applications 115 (7) 1073 (2005)
https://doi.org/10.1016/j.spa.2005.02.004