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):

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)
DOI: 10.1007/978-3-319-22977-5_30-1
See this article

Nonconforming Discontinuous Galerkin Methods for Nonlocal Variational Problems

Xiaochuan Tian and Qiang Du
SIAM Journal on Numerical Analysis 53 (2) 762 (2015)
DOI: 10.1137/140978831
See this article

Nonlocal Constrained Value Problems for a Linear Peridynamic Navier Equation

Tadele Mengesha and Qiang Du
Journal of Elasticity 116 (1) 27 (2014)
DOI: 10.1007/s10659-013-9456-z
See this article

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)
DOI: 10.1002/num.22179
See this article

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)
DOI: 10.1016/S0034-4877(17)30061-7
See this article

A fast Galerkin method with efficient matrix assembly and storage for a peridynamic model

Hong Wang and Hao Tian
Journal of Computational Physics (2012)
DOI: 10.1016/j.jcp.2012.07.045
See this article

Structural Nonlinear Dynamics and Diagnosis

Raouf A. Ibrahim
Springer Proceedings in Physics, Structural Nonlinear Dynamics and Diagnosis 168 1 (2015)
DOI: 10.1007/978-3-319-19851-4_1
See this article

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

Qiang Du and Tadele Mengesha
Discrete and Continuous Dynamical Systems - Series B 18 (5) 1415 (2013)
DOI: 10.3934/dcdsb.2013.18.1415
See this article

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

Qiang Du and Jiang Yang
SIAM Journal on Numerical Analysis 54 (3) 1899 (2016)
DOI: 10.1137/15M1039857
See this article

Existence for Nonlocal Variational Problems in Peridynamics

José C. Bellido and Carlos Mora-Corral
SIAM Journal on Mathematical Analysis 46 (1) 890 (2014)
DOI: 10.1137/130911548
See this article

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)
DOI: 10.1016/j.cma.2014.01.026
See this article

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)
DOI: 10.1137/120871638
See this article

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)
DOI: 10.3934/dcdsb.2015.20.1315
See this article

Optimal Distributed Control of Nonlocal Steady Diffusion Problems

Marta D'Elia and Max Gunzburger
SIAM Journal on Control and Optimization 52 (1) 243 (2014)
DOI: 10.1137/120897857
See this article

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)
DOI: 10.1137/140963066
See this article

Analysis and Comparison of Different Approximations to Nonlocal Diffusion and Linear Peridynamic Equations

Xiaochuan Tian and Qiand Du
SIAM Journal on Numerical Analysis 51 (6) 3458 (2013)
DOI: 10.1137/13091631X
See this article

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

Etienne Emmrich and Dimitri Puhst
Computational Methods in Applied Mathematics (2015)
DOI: 10.1515/cmam-2015-0020
See this article

On the variational limit of a class of nonlocal functionals related to peridynamics

Tadele Mengesha and Qiang Du
Nonlinearity 28 (11) 3999 (2015)
DOI: 10.1088/0951-7715/28/11/3999
See this article

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)
DOI: 10.1016/j.jmaa.2015.04.026
See this article

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)
DOI: 10.1080/01630563.2017.1320674
See this article

The Cauchy problem for a one-dimensional nonlinear elastic peridynamic model

H.A. Erbay, A. Erkip and G.M. Muslu
Journal of Differential Equations 252 (8) 4392 (2012)
DOI: 10.1016/j.jde.2012.01.008
See this article

A fast Galerkin method with efficient matrix assembly and storage for a peridynamic model

Hong Wang and Hao Tian
Journal of Computational Physics 231 (23) 7730 (2012)
DOI: 10.1016/j.jcp.2012.06.009
See this article

Dirichlet’s principle and wellposedness of solutions for a nonlocal Laplacian system

Brittney Hinds and Petronela Radu
Applied Mathematics and Computation 219 (4) 1411 (2012)
DOI: 10.1016/j.amc.2012.07.045
See this article

Analysis of the Volume-Constrained Peridynamic Navier Equation of Linear Elasticity

Qiang Du, Max Gunzburger, R. B. Lehoucq and Kun Zhou
Journal of Elasticity 113 (2) 193 (2013)
DOI: 10.1007/s10659-012-9418-x
See this article

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)
DOI: 10.1016/j.cma.2013.05.018
See this article

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)
DOI: 10.1016/j.cma.2016.07.023
See this article

Measure-valued and weak solutions to the nonlinear peridynamic model in nonlocal elastodynamics

Etienne Emmrich and Dimitri Puhst
Nonlinearity 28 (1) 285 (2015)
DOI: 10.1088/0951-7715/28/1/285
See this article

On a class of nonlocal wave equations from applications

Horst Reinhard Beyer, Burak Aksoylu and Fatih Celiker
Journal of Mathematical Physics 57 (6) 062902 (2016)
DOI: 10.1063/1.4953252
See this article

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)
DOI: 10.1016/j.cma.2017.03.020
See this article

A Conforming DG Method for Linear Nonlocal Models with Integrable Kernels

Qiang Du and Xiaobo Yin
Journal of Scientific Computing 80 (3) 1913 (2019)
DOI: 10.1007/s10915-019-01006-0
See this article

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)
DOI: 10.1016/j.cma.2016.08.020
See this article

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)
DOI: 10.1016/j.amc.2014.09.113
See this article

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)
DOI: 10.1142/S0218202512500546
See this article

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)
DOI: 10.1142/S1758825118500035
See this article

Handbook of Structural Life Assessment

Handbook of Structural Life Assessment 767 (2017)
DOI: 10.1002/9781119135470.refs
See this article

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)
DOI: 10.1155/2013/631074
See this article

NONLOCAL KORN-TYPE CHARACTERIZATION OF SOBOLEV VECTOR FIELDS

TADELE MENGESHA
Communications in Contemporary Mathematics 14 (04) 1250028 (2012)
DOI: 10.1142/S0219199712500289
See this article

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)
DOI: 10.1007/s00033-019-1136-9
See this article

Static and Dynamic Green’s Functions in Peridynamics

Linjuan Wang, Jifeng Xu and Jianxiang Wang
Journal of Elasticity 126 (1) 95 (2017)
DOI: 10.1007/s10659-016-9583-4
See this article

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)
DOI: 10.1016/j.ijimpeng.2016.09.003
See this article

Fractional Korn and Hardy-type inequalities for vector fields in half space

Tadele Mengesha
Communications in Contemporary Mathematics 21 (07) 1850055 (2019)
DOI: 10.1142/S0219199718500554
See this article

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)
DOI: 10.1137/130942644
See this article

Conditioning Analysis of Nonlocal Integral Operators in Fractional Sobolev Spaces

Burak Aksoylu and Zuhal Unlu
SIAM Journal on Numerical Analysis 52 (2) 653 (2014)
DOI: 10.1137/13092407X
See this article

Analysis and Approximation of Nonlocal Diffusion Problems with Volume Constraints

Qiang Du, Max Gunzburger, R. B. Lehoucq and Kun Zhou
SIAM Review 54 (4) 667 (2012)
DOI: 10.1137/110833294
See this article

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 (2017)
DOI: 10.1007/s10915-017-0456-1
See this article

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 (2019)
DOI: 10.1002/mma.5701
See this article

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)
DOI: 10.1002/nme.5791
See this article

An accurate and asymptotically compatible collocation scheme for nonlocal diffusion problems

Xiaoping Zhang, Jiming Wu and Lili Ju
Applied Numerical Mathematics 133 52 (2018)
DOI: 10.1016/j.apnum.2017.11.007
See this article

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

Yue Yu, Fabiano F. Bargos, Huaiqian You, et al.
Computer Methods in Applied Mechanics and Engineering 340 905 (2018)
DOI: 10.1016/j.cma.2018.06.008
See this article

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) (2017)
DOI: 10.1515/cmam-2017-0029
See this article

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)
DOI: 10.1016/j.cma.2015.02.008
See this article

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)
DOI: 10.1137/17M1124012
See this article

Wellposedness of a nonlinear peridynamic model

Giuseppe Maria Coclite, Serena Dipierro, Francesco Maddalena and Enrico Valdinoci
Nonlinearity 32 (1) 1 (2019)
DOI: 10.1088/1361-6544/aae71b
See this article

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)
DOI: 10.1007/978-3-319-58729-5_30
See this article

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)
DOI: 10.1007/978-3-319-58729-5_44
See this article

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)
DOI: 10.1137/18M1189294
See this article

Exploiting multilevel Toeplitz structures in high dimensional nonlocal diffusion

Christian Vollmann and Volker Schulz
Computing and Visualization in Science 20 (1-2) 29 (2019)
DOI: 10.1007/s00791-018-00306-6
See this article

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)
DOI: 10.1016/j.jcp.2016.11.028
See this article

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)
DOI: 10.1016/j.camwa.2017.02.008
See this article

On a nonlocal extension of differentiation

Ravi Shankar
Journal of Mathematical Analysis and Applications 440 (2) 516 (2016)
DOI: 10.1016/j.jmaa.2016.03.054
See this article

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)
DOI: 10.4208/cicp.OA-2016-0033
See this article

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

Qiang Du, Yunzhe Tao, Xiaochuan Tian and Jiang Yang
IMA Journal of Numerical Analysis 39 (2) 607 (2019)
DOI: 10.1093/imanum/dry011
See this article

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)
DOI: 10.1137/18M118236X
See this article

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)
DOI: 10.1007/978-3-642-32979-1_3
See this article