Xiaochuan Tian
Xiaochuan Tian
Verified email at math.utexas.edu - Homepage
TitleCited byYear
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
1212013
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
992014
Nonconforming discontinuous Galerkin methods for nonlocal variational problems
X Tian, Q Du
SIAM Journal on Numerical Analysis 53 (2), 762-781, 2015
232015
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
162017
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
162016
A peridynamic model of fracture mechanics with bond-breaking
Q Du, Y Tao, X Tian
Journal of Elasticity 132 (2), 197-218, 2018
152018
Trace theorems for some nonlocal function spaces with heterogeneous localization
X Tian, Q Du
SIAM Journal on Mathematical Analysis 49 (2), 1621-1644, 2017
152017
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 (6), 1363-1380, 2016
142016
Robust discretization of nonlocal models related to peridynamics
Q Du, X Tian
Meshfree methods for partial differential equations VII, 97-113, 2015
132015
Asymptotically compatible schemes for peridynamics based on numerical quadratures
Q Du, X Tian
ASME 2014 International Mechanical Engineering Congress and Exposition …, 2014
122014
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
92018
Mathematics of Smoothed Particle Hydrodynamics: A Study via Nonlocal Stokes Equations
Q Du, X Tian
Foundations of Computational Mathematics, 1-26, 2019
6*2019
Nonlocal models with a finite range of nonlocal interactions
X Tian
Columbia University, 2017
62017
A class of high order nonlocal operators
X Tian, Q Du
Archive for Rational Mechanics and Analysis 222 (3), 1521-1553, 2016
62016
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
52018
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, 2018
32018
Nonlocal criteria for compactness in the space of vector fields
Q Du, T Mengesha, X Tian
arXiv preprint arXiv:1801.08000, 2018
22018
Heterogeneously localized nonlocal operators, boundary traces and variational problems
Q DU, X TIAN
Proceedings of the International Congress of Chinese Mathematicians …, 2018
22018
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
12019
Super-convergence of reproducing kernel approximation
Y Leng, X Tian, JT Foster
Computer Methods in Applied Mechanics and Engineering 352, 488--507, 2019
12019
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Articles 1–20