EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues ESAIM: M2AN, 45 2 (2011) 217-234 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:

Tensor-involved peridynamics: A unified framework for isotropic and anisotropic materials

Hao Tian, Jinlong Shao, Chenguang Liu, Shuo Liu and Xu Guo
Engineering Fracture Mechanics 325 111294 (2025)
https://doi.org/10.1016/j.engfracmech.2025.111294

Numerical approximation and simulation of a Volterra integro‐differential equation with a peridynamic differential operator

Yan Zhu, Tiantian Dong, Xiangcheng Zheng, Yiqun Li, Sihao Jia and Xu Guo
ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik 105 (3) (2025)
https://doi.org/10.1002/zamm.202400619

Nonlocal Problems with Local Boundary Conditions II: Green’s Identities and Regularity of Solutions

James M. Scott and Qiang Du
SIAM Journal on Mathematical Analysis 57 (1) 404 (2025)
https://doi.org/10.1137/24M1643505

Asymptotically compatible schemes for nonlocal Ohta–Kawasaki model

Wangbo Luo and Yanxiang Zhao
Numerical Methods for Partial Differential Equations 40 (6) (2024)
https://doi.org/10.1002/num.23143

Heterogeneous peridynamic neural operators: Discover biotissue constitutive law and microstructure from digital image correlation measurements

Siavash Jafarzadeh, Stewart Silling, Lu Zhang, Colton Ross, Chung-Hao Lee, S. M. Rakibur Rahman, Shuodao Wang and Yue Yu
Foundations of Data Science (2024)
https://doi.org/10.3934/fods.2024041

Stability and convergence analysis of high-order numerical schemes with DtN-type absorbing boundary conditions for nonlocal wave equations

Jihong Wang, Jerry Zhijian Yang and Jiwei Zhang
IMA Journal of Numerical Analysis 44 (1) 604 (2024)
https://doi.org/10.1093/imanum/drad016

A novel bond-based nonlocal diffusion model with matrix-valued coefficients in non-divergence form and its collocation discretization

Hao Tian, Junke Lu and Lili Ju
Computers & Mathematics with Applications 173 33 (2024)
https://doi.org/10.1016/j.camwa.2024.08.002

A review of peridynamic theory and nonlocal operators along with their computer implementations

Mehmet Dorduncu, Huilong Ren, Xiaoying Zhuang, Stewart Silling, Erdogan Madenci and Timon Rabczuk
Computers & Structures 299 107395 (2024)
https://doi.org/10.1016/j.compstruc.2024.107395

A Numerical Framework for Nonlinear Peridynamics on Two-Dimensional Manifolds Based on Implicit P-(EC)\(^{ {\boldsymbol k}}\) Schemes

Alessandro Coclite, Giuseppe M. Coclite, Francesco Maddalena and Tiziano Politi
SIAM Journal on Numerical Analysis 62 (2) 622 (2024)
https://doi.org/10.1137/22M1498942

Bond‐based peridynamics model of 3‐point bend tests of ceramic‐composite interfaces

Angelo Battistini, Thomas A. Haynes, Lloyd Jones and Mark R. Wenman
Journal of the American Ceramic Society 107 (9) 6004 (2024)
https://doi.org/10.1111/jace.19905

Shape optimization for interface identification in nonlocal models

Matthias Schuster, Christian Vollmann and Volker Schulz
Computational Optimization and Applications 88 (3) 963 (2024)
https://doi.org/10.1007/s10589-024-00575-7

OBMeshfree: An Optimization-Based Meshfree Solver for Nonlocal Diffusion and Peridynamics Models

Yiming Fan, Huaiqian You and Yue Yu
Journal of Peridynamics and Nonlocal Modeling 6 (1) 4 (2024)
https://doi.org/10.1007/s42102-023-00099-4

Nonlocal Problems with Local Boundary Conditions I: Function Spaces and Variational Principles

James M. Scott and Qiang Du
SIAM Journal on Mathematical Analysis 56 (3) 4185 (2024)
https://doi.org/10.1137/23M1588111

A stable and high-order numerical scheme with discrete DtN-type artificial boundary conditions for a 2D peridynamic diffusion model

Jihong Wang, Yana Di, Jerry Zhijian Yang and Jiwei Zhang
Computers & Mathematics with Applications 158 1 (2024)
https://doi.org/10.1016/j.camwa.2024.01.006

Nonlocal-to-local limit in linearized viscoelasticity

Manuel Friedrich, Manuel Seitz and Ulisse Stefanelli
Communications in Applied and Industrial Mathematics 15 (1) 1 (2024)
https://doi.org/10.2478/caim-2024-0001

Numerical analysis of a class of penalty discontinuous Galerkin methods for nonlocal diffusion problems

Qiang Du, Lili Ju, Jianfang Lu and Xiaochuan Tian
ESAIM: Mathematical Modelling and Numerical Analysis 58 (5) 2035 (2024)
https://doi.org/10.1051/m2an/2024064

On the fractional Korn inequality in bounded domains: Counterexamples to the case ps < 1

Davit Harutyunyan and Hayk Mikayelyan
Advances in Nonlinear Analysis 12 (1) (2023)
https://doi.org/10.1515/anona-2022-0283

$ L^{p} $ compactness criteria with an application to variational convergence of some nonlocal energy functionals

Qiang Du, Tadele Mengesha and Xiaochuan Tian
Mathematics in Engineering 5 (6) 1 (2023)
https://doi.org/10.3934/mine.2023097

Distal and non-symmetrical crack nucleation in delamination of plates via dimensionally-reduced peridynamics

R. Cavuoto, A. Cutolo, K. Dayal, L. Deseri and M. Fraldi
Journal of the Mechanics and Physics of Solids 172 105189 (2023)
https://doi.org/10.1016/j.jmps.2022.105189

Bayesian Nonlocal Operator Regression: A Data-Driven Learning Framework of Nonlocal Models with Uncertainty Quantification

Yiming Fan, Marta D’Elia, Yue Yu, Habib N. Najm and Stewart Silling
Journal of Engineering Mechanics 149 (8) (2023)
https://doi.org/10.1061/JENMDT.EMENG-6994

Towards a unified nonlocal, peridynamics framework for the coarse-graining of molecular dynamics data with fractures

H. Q. You, X. Xu, Y. Yu, S. Silling, M. D’Elia and J. Foster
Applied Mathematics and Mechanics 44 (7) 1125 (2023)
https://doi.org/10.1007/s10483-023-2996-8

Solvability of Singular Equations of Peridynamics on Two-Dimensional Periodic Structures

Shavkat Alimov and Asal Yuldasheva
Journal of Peridynamics and Nonlocal Modeling 5 (2) 241 (2023)
https://doi.org/10.1007/s42102-021-00070-1

A Variational Theory of Convolution-Type Functionals

Roberto Alicandro, Nadia Ansini, Andrea Braides, Andrey Piatnitski and Antonio Tribuzio
SpringerBriefs on PDEs and Data Science, A Variational Theory of Convolution-Type Functionals 1 (2023)
https://doi.org/10.1007/978-981-99-0685-7_1

A comparative review of peridynamics and phase-field models for engineering fracture mechanics

Patrick Diehl, Robert Lipton, Thomas Wick and Mayank Tyagi
Computational Mechanics 69 (6) 1259 (2022)
https://doi.org/10.1007/s00466-022-02147-0

An asymptotically compatible probabilistic collocation method for randomly heterogeneous nonlocal problems

Yiming Fan, Xiaochuan Tian, Xiu Yang, et al.
Journal of Computational Physics 465 111376 (2022)
https://doi.org/10.1016/j.jcp.2022.111376

A data-driven peridynamic continuum model for upscaling molecular dynamics

Huaiqian You, Yue Yu, Stewart Silling and Marta D’Elia
Computer Methods in Applied Mechanics and Engineering 389 114400 (2022)
https://doi.org/10.1016/j.cma.2021.114400

A meshfree peridynamic model for brittle fracture in randomly heterogeneous materials

Yiming Fan, Huaiqian You, Xiaochuan Tian, Xiu Yang, Xingjie Li, Naveen Prakash and Yue Yu
Computer Methods in Applied Mechanics and Engineering 399 115340 (2022)
https://doi.org/10.1016/j.cma.2022.115340

A nonlocal nonlinear stiffened shell theory with stiffeners modeled as geometrically-exact beams

Qi Zhang, Shaofan Li, A-Man Zhang, Yuxiang Peng and Kun Zhou
Computer Methods in Applied Mechanics and Engineering 397 115150 (2022)
https://doi.org/10.1016/j.cma.2022.115150

An asymptotically compatible approach for Neumann-type boundary condition on nonlocal problems

Huaiqian You, Xin Yang Lu, Nathaniel Trask and Yue Yu
ESAIM: Mathematical Modelling and Numerical Analysis 55 S811 (2021)
https://doi.org/10.1051/m2an/2020058

An asymptotically compatible treatment of traction loading in linearly elastic peridynamic fracture

Yue Yu, Huaiqian You and Nathaniel Trask
Computer Methods in Applied Mechanics and Engineering 377 113691 (2021)
https://doi.org/10.1016/j.cma.2021.113691

Maximum principle preserving finite difference scheme for 1-D nonlocal-to-local diffusion problems

Amanda Gute and Xingjie Helen Li
Results in Applied Mathematics 12 100211 (2021)
https://doi.org/10.1016/j.rinam.2021.100211

Nonlocal gradient operators with a nonspherical interaction neighborhood and their applications

Hwi Lee and Qiang Du
ESAIM: Mathematical Modelling and Numerical Analysis 54 (1) 105 (2020)
https://doi.org/10.1051/m2an/2019053

A spectral collocation method for nonlocal diffusion equations with volume constrained boundary conditions

Hao Tian, Jing Zhang and Lili Ju
Applied Mathematics and Computation 370 124930 (2020)
https://doi.org/10.1016/j.amc.2019.124930

An asymptotically compatible approach for Neumann-type boundary condition on nonlocal problems

Huaiqian You, XinYang Lu, Nathaniel Task and Yue Yu
ESAIM: Mathematical Modelling and Numerical Analysis 54 (4) 1373 (2020)
https://doi.org/10.1051/m2an/2019089

Helmholtz-Hodge Decompositions in the Nonlocal Framework

Marta D’Elia, Cynthia Flores, Xingjie Li, Petronela Radu and Yue Yu
Journal of Peridynamics and Nonlocal Modeling 2 (4) 401 (2020)
https://doi.org/10.1007/s42102-020-00035-w

Asymptotically Compatible Schemes for Robust Discretization of Parametrized Problems with Applications to Nonlocal Models

Xiaochuan Tian and Qiang Du
SIAM Review 62 (1) 199 (2020)
https://doi.org/10.1137/19M1296720

An asymptotically compatible formulation for local-to-nonlocal coupling problems without overlapping regions

Huaiqian You, Yue Yu and David Kamensky
Computer Methods in Applied Mechanics and Engineering 366 113038 (2020)
https://doi.org/10.1016/j.cma.2020.113038

The solvability of a strongly-coupled nonlocal system of equations

Tadele Mengesha and James M. Scott
Journal of Mathematical Analysis and Applications 486 (2) 123919 (2020)
https://doi.org/10.1016/j.jmaa.2020.123919

Existence and approximation of nonlocal optimal design problems driven by parabolic equations

Fuensanta Andrés, Julio Muñoz and Jesús Rosado
Mathematical Methods in the Applied Sciences 42 (18) 6049 (2019)
https://doi.org/10.1002/mma.5701

A Potential Space Estimate for Solutions of Systems of Nonlocal Equations in Peridynamics

James Scott and Tadele Mengesha
SIAM Journal on Mathematical Analysis 51 (1) 86 (2019)
https://doi.org/10.1137/18M1189294

The Galerkin–Fourier method for the study of nonlocal parabolic equations

Fuensanta Andrés and Julio Muñoz
Zeitschrift für angewandte Mathematik und Physik 70 (4) (2019)
https://doi.org/10.1007/s00033-019-1136-9

Asymptotically compatible discretization of multidimensional nonlocal diffusion models and approximation of nonlocal Green’s functions

Jiang Yang, Xiaochuan Tian, Yunzhe Tao and Qiang Du
IMA Journal of Numerical Analysis 39 (2) 607 (2019)
https://doi.org/10.1093/imanum/dry011

Maximum Principle Preserving Exponential Time Differencing Schemes for the Nonlocal Allen--Cahn Equation

Qiang Du, Lili Ju, Xiao Li and Zhonghua Qiao
SIAM Journal on Numerical Analysis 57 (2) 875 (2019)
https://doi.org/10.1137/18M118236X

Handbook of Nonlocal Continuum Mechanics for Materials and Structures

Prashant K. Jha and Robert Lipton
Handbook of Nonlocal Continuum Mechanics for Materials and Structures 1457 (2019)
https://doi.org/10.1007/978-3-319-58729-5_44

Handbook of Nonlocal Continuum Mechanics for Materials and Structures

Marta D’Elia, Qiang Du and Max Gunzburger
Handbook of Nonlocal Continuum Mechanics for Materials and Structures 1197 (2019)
https://doi.org/10.1007/978-3-319-58729-5_30

Exploiting multilevel Toeplitz structures in high dimensional nonlocal diffusion

Christian Vollmann and Volker Schulz
Computing and Visualization in Science 20 (1-2) 29 (2019)
https://doi.org/10.1007/s00791-018-00306-6

Wellposedness of a nonlinear peridynamic model

Giuseppe Maria Coclite, Serena Dipierro, Francesco Maddalena and Enrico Valdinoci
Nonlinearity 32 (1) 1 (2019)
https://doi.org/10.1088/1361-6544/aae71b

Numerical convergence of nonlinear nonlocal continuum models to local elastodynamics

Prashant K. Jha and Robert Lipton
International Journal for Numerical Methods in Engineering 114 (13) 1389 (2018)
https://doi.org/10.1002/nme.5791

A Quasi-nonlocal Coupling Method for Nonlocal and Local Diffusion Models

Qiang Du, Xingjie Helen Li, Jianfeng Lu and Xiaochuan Tian
SIAM Journal on Numerical Analysis 56 (3) 1386 (2018)
https://doi.org/10.1137/17M1124012

An accurate and asymptotically compatible collocation scheme for nonlocal diffusion problems

Xiaoping Zhang, Jiming Wu and Lili Ju
Applied Numerical Mathematics 133 52 (2018)
https://doi.org/10.1016/j.apnum.2017.11.007

Handbook of Nonlocal Continuum Mechanics for Materials and Structures

Prashant K. Jha and Robert Lipton
Handbook of Nonlocal Continuum Mechanics for Materials and Structures 1 (2018)
https://doi.org/10.1007/978-3-319-22977-5_44-1

Free and Forced Vibration Analysis of Peridynamic Finite Bar

Jingkai Chen, Ye Tian and Xuezheng Cui
International Journal of Applied Mechanics 10 (01) 1850003 (2018)
https://doi.org/10.1142/S1758825118500035

Handbook of Nonlocal Continuum Mechanics for Materials and Structures

Marta D’Elia, Qiang Du and Max Gunzburger
Handbook of Nonlocal Continuum Mechanics for Materials and Structures 1 (2018)
https://doi.org/10.1007/978-3-319-22977-5_30-1

A Fast Finite Difference Method for a Continuous Static Linear Bond-Based Peridynamics Model of Mechanics

Zhengguang Liu and Xiaoli Li
Journal of Scientific Computing 74 (2) 728 (2018)
https://doi.org/10.1007/s10915-017-0456-1

A partitioned coupling framework for peridynamics and classical theory: Analysis and simulations

Yue Yu, Fabiano F. Bargos, Huaiqian You, Michael L. Parks, Marco L. Bittencourt and George E. Karniadakis
Computer Methods in Applied Mechanics and Engineering 340 905 (2018)
https://doi.org/10.1016/j.cma.2018.06.008

Theoretical Foundations of Incorporating Local Boundary Conditions into Nonlocal Problems

Burak Aksoylu, Horst Reinhard Beyer and Fatih Celiker
Reports on Mathematical Physics 80 (1) 39 (2017)
https://doi.org/10.1016/S0034-4877(17)30061-7

Artificial Boundary Conditions for Nonlocal Heat Equations on Unbounded Domain

Wei Zhang, Jiang Yang, Jiwei Zhang and Qiang Du
Communications in Computational Physics 21 (1) 16 (2017)
https://doi.org/10.4208/cicp.OA-2016-0033

A fast discontinuous finite element discretization for the space‐time fractional diffusion‐wave equation

Zhengguang Liu, Aijie Cheng and Xiaoli Li
Numerical Methods for Partial Differential Equations 33 (6) 2043 (2017)
https://doi.org/10.1002/num.22179

An hp-Galerkin method with fast solution for linear peridynamic models in one dimension

Zhengguang Liu, Aijie Cheng and Hong Wang
Computers & Mathematics with Applications 73 (7) 1546 (2017)
https://doi.org/10.1016/j.camwa.2017.02.008

A conservative nonlocal convection–diffusion model and asymptotically compatible finite difference discretization

Hao Tian, Lili Ju and Qiang Du
Computer Methods in Applied Mechanics and Engineering 320 46 (2017)
https://doi.org/10.1016/j.cma.2017.03.020

Nonlocal Convection-Diffusion Problems on Bounded Domains and Finite-Range Jump Processes

Marta D’Elia, Qiang Du, Max Gunzburger and Richard Lehoucq
Computational Methods in Applied Mathematics 17 (4) 707 (2017)
https://doi.org/10.1515/cmam-2017-0029

Fast and accurate implementation of Fourier spectral approximations of nonlocal diffusion operators and its applications

Qiang Du and Jiang Yang
Journal of Computational Physics 332 118 (2017)
https://doi.org/10.1016/j.jcp.2016.11.028

A 3D discontinuous Galerkin finite element method with the bond-based peridynamics model for dynamic brittle failure analysis

Bo Ren, C.T. Wu and E. Askari
International Journal of Impact Engineering 99 14 (2017)
https://doi.org/10.1016/j.ijimpeng.2016.09.003

Application and Implementation of Incorporating Local Boundary Conditions into Nonlocal Problems

Burak Aksoylu, Horst Reinhard Beyer and Fatih Celiker
Numerical Functional Analysis and Optimization 38 (9) 1077 (2017)
https://doi.org/10.1080/01630563.2017.1320674

A fast collocation method for a static bond-based linear peridynamic model

Xuhao Zhang and Hong Wang
Computer Methods in Applied Mechanics and Engineering (2016)
https://doi.org/10.1016/j.cma.2016.08.020

Robust a posteriori stress analysis for quadrature collocation approximations of nonlocal models via nonlocal gradients

Qiang Du, Yunzhe Tao, Xiaochuan Tian and Jiang Yang
Computer Methods in Applied Mechanics and Engineering 310 605 (2016)
https://doi.org/10.1016/j.cma.2016.07.023

Asymptotically Compatible Fourier Spectral Approximations of Nonlocal Allen--Cahn Equations

Qiang Du and Jiang Yang
SIAM Journal on Numerical Analysis 54 (3) 1899 (2016)
https://doi.org/10.1137/15M1039857

On a class of nonlocal wave equations from applications

Horst Reinhard Beyer, Burak Aksoylu and Fatih Celiker
Journal of Mathematical Physics 57 (6) (2016)
https://doi.org/10.1063/1.4953252

Survey of Existence Results in Nonlinear Peridynamics in Comparison with Local Elastodynamics

Etienne Emmrich and Dimitri Puhst
Computational Methods in Applied Mathematics 15 (4) 483 (2015)
https://doi.org/10.1515/cmam-2015-0020

Nonlocal optimal design: A new perspective about the approximation of solutions in optimal design

Fuensanta Andrés and Julio Muñoz
Journal of Mathematical Analysis and Applications 429 (1) 288 (2015)
https://doi.org/10.1016/j.jmaa.2015.04.026

A Type of Nonlocal Elliptic Problem: Existence and Approximation Through a Galerkin--Fourier Method

Fuensanta Andrés and Julio Mun͂oz
SIAM Journal on Mathematical Analysis 47 (1) 498 (2015)
https://doi.org/10.1137/140963066

Nonlocal convection–diffusion problems and finite element approximations

Hao Tian, Lili Ju and Qiang Du
Computer Methods in Applied Mechanics and Engineering 289 60 (2015)
https://doi.org/10.1016/j.cma.2015.02.008

Nonconforming Discontinuous Galerkin Methods for Nonlocal Variational Problems

Xiaochuan Tian and Qiang Du
SIAM Journal on Numerical Analysis 53 (2) 762 (2015)
https://doi.org/10.1137/140978831

Stability and convergence of time-stepping methods for a nonlocal model for diffusion

Max Gunzburger and Qingguang Guan
Discrete and Continuous Dynamical Systems - Series B 20 (5) 1315 (2015)
https://doi.org/10.3934/dcdsb.2015.20.1315

Meshfree Methods for Partial Differential Equations VII

Qiang Du and Xiaochuan Tian
Lecture Notes in Computational Science and Engineering, Meshfree Methods for Partial Differential Equations VII 100 97 (2015)
https://doi.org/10.1007/978-3-319-06898-5_6

A fast and faithful collocation method with efficient matrix assembly for a two-dimensional nonlocal diffusion model

Hong Wang and Hao Tian
Computer Methods in Applied Mechanics and Engineering 273 19 (2014)
https://doi.org/10.1016/j.cma.2014.01.026

Circulant preconditioned iterative methods for peridynamic model simulation

Xian-Ming Gu, Ting-Zhu Huang, Xi-Le Zhao, et al.
Applied Mathematics and Computation 248 470 (2014)
https://doi.org/10.1016/j.amc.2014.09.113

Existence for Nonlocal Variational Problems in Peridynamics

José C. Bellido and Carlos Mora-Corral
SIAM Journal on Mathematical Analysis 46 (1) 890 (2014)
https://doi.org/10.1137/130911548

Optimal Distributed Control of Nonlocal Steady Diffusion Problems

Marta D'Elia and Max Gunzburger
SIAM Journal on Control and Optimization 52 (1) 243 (2014)
https://doi.org/10.1137/120897857

Conditioning Analysis of Nonlocal Integral Operators in Fractional Sobolev Spaces

Burak Aksoylu and Zuhal Unlu
SIAM Journal on Numerical Analysis 52 (2) 653 (2014)
https://doi.org/10.1137/13092407X

Asymptotically Compatible Schemes and Applications to Robust Discretization of Nonlocal Models

Xiaochuan Tian and Qiang Du
SIAM Journal on Numerical Analysis 52 (4) 1641 (2014)
https://doi.org/10.1137/130942644

Interface problems in nonlocal diffusion and sharp transitions between local and nonlocal domains

Pablo Seleson, Max Gunzburger and Michael L. Parks
Computer Methods in Applied Mechanics and Engineering 266 185 (2013)
https://doi.org/10.1016/j.cma.2013.05.018

Analysis of a scalar nonlocal peridynamic model with a sign changing kernel

Tadele Mengesha and Qiang Du
Discrete & Continuous Dynamical Systems - B 18 (5) 1415 (2013)
https://doi.org/10.3934/dcdsb.2013.18.1415

A NONLOCAL VECTOR CALCULUS, NONLOCAL VOLUME-CONSTRAINED PROBLEMS, AND NONLOCAL BALANCE LAWS

QIANG DU, MAX GUNZBURGER, R. B. LEHOUCQ and KUN ZHOU
Mathematical Models and Methods in Applied Sciences 23 (03) 493 (2013)
https://doi.org/10.1142/S0218202512500546

A Convergent Adaptive Finite Element Algorithm for Nonlocal Diffusion and Peridynamic Models

Qiang Du, Li Tian and Xuying Zhao
SIAM Journal on Numerical Analysis 51 (2) 1211 (2013)
https://doi.org/10.1137/120871638

Damage and Failure Process of Concrete Structure under Uniaxial Compression Based on Peridynamics Modeling

Feng Shen, Qing Zhang and Dan Huang
Mathematical Problems in Engineering 2013 1 (2013)
https://doi.org/10.1155/2013/631074

Meshfree Methods for Partial Differential Equations VI

Etienne Emmrich, Richard B. Lehoucq and Dimitri Puhst
Lecture Notes in Computational Science and Engineering, Meshfree Methods for Partial Differential Equations VI 89 45 (2013)
https://doi.org/10.1007/978-3-642-32979-1_3