Xiaochuan Tian
Xiaochuan Tian
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Analysis and comparison of different approximations to nonlocal diffusion and linear peridynamic equations
X Tian, Q Du
SIAM Journal on Numerical Analysis 51 (6), 3458-3482, 2013
Asymptotically compatible schemes and applications to robust discretization of nonlocal models
X Tian, Q Du
SIAM Journal on Numerical Analysis 52 (4), 1641-1665, 2014
Numerical methods for nonlocal and fractional models
M D’Elia, Q Du, C Glusa, M Gunzburger, X Tian, Z Zhou
Acta Numerica 29, 1-124, 2020
Nonlocal diffusion and peridynamic models with Neumann type constraints and their numerical approximations
Y Tao, X Tian, Q Du
Applied Mathematics and Computation 305, 282-298, 2017
A review of local-to-nonlocal coupling methods in nonlocal diffusion and nonlocal mechanics
M D’Elia, X Li, P Seleson, X Tian, Y Yu
Journal of Peridynamics and Nonlocal Modeling, 1-50, 2021
A peridynamic model of fracture mechanics with bond-breaking
Q Du, Y Tao, X Tian
Journal of Elasticity 132, 197-218, 2018
Nonconforming discontinuous Galerkin methods for nonlocal variational problems
X Tian, Q Du
SIAM Journal on Numerical Analysis 53 (2), 762-781, 2015
A physically consistent, flexible, and efficient strategy to convert local boundary conditions into nonlocal volume constraints
M D'Elia, X Tian, Y Yu
SIAM Journal on Scientific Computing 42 (4), A1935-A1949, 2020
Trace theorems for some nonlocal function spaces with heterogeneous localization
X Tian, Q Du
SIAM Journal on Mathematical Analysis 49 (2), 1621-1644, 2017
Asymptotically compatible schemes for the approximation of fractional Laplacian and related nonlocal diffusion problems on bounded domains
X Tian, Q Du, M Gunzburger
Advances in Computational Mathematics 42, 1363-1380, 2016
Asymptotically compatible reproducing kernel collocation and meshfree integration for nonlocal diffusion
Y Leng, X Tian, N Trask, JT Foster
SIAM Journal on Numerical Analysis 59 (1), 88-118, 2021
Stability of nonlocal Dirichlet integrals and implications for peridynamic correspondence material modeling
Q Du, X Tian
SIAM Journal on Applied Mathematics 78 (3), 1536-1552, 2018
A quasi-nonlocal coupling method for nonlocal and local diffusion models
Q Du, XH Li, J Lu, X Tian
SIAM Journal on Numerical Analysis 56 (3), 1386-1404, 2018
Mathematics of smoothed particle hydrodynamics: A study via nonlocal stokes equations
Q Du, X Tian
Foundations of Computational Mathematics 20 (4), 801-826, 2020
Asymptotically compatible discretization of multidimensional nonlocal diffusion models and approximation of nonlocal Green’s functions
Q Du, Y Tao, X Tian, J Yang
IMA Journal of numerical analysis 39 (2), 607-625, 2019
Robust a posteriori stress analysis for quadrature collocation approximations of nonlocal models via nonlocal gradients
Q Du, Y Tao, X Tian, J Yang
Computer Methods in Applied Mechanics and Engineering 310, 605-627, 2016
Asymptotically compatible schemes for robust discretization of parametrized problems with applications to nonlocal models
X Tian, Q Du
SIAM Review 62 (1), 199-227, 2020
Nonlocal models with heterogeneous localization and their application to seamless local-nonlocal coupling
Y Tao, X Tian, Q Du
Multiscale Modeling & Simulation 17 (3), 1052-1075, 2019
The double adaptivity paradigm:(How to circumvent the discrete inf–sup conditions of Babuška and Brezzi)
L Demkowicz, T Führer, N Heuer, X Tian
Computers & Mathematics with Applications 95, 41-66, 2021
Multiscale modeling, homogenization and nonlocal effects: Mathematical and computational issues
Q Du, B Engquist, X Tian
Contemporary mathematics 754, 115-140, 2020
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