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
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
Nonconforming discontinuous Galerkin methods for nonlocal variational problems
X Tian, Q Du
SIAM Journal on Numerical Analysis 53 (2), 762-781, 2015
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
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
A peridynamic model of fracture mechanics with bond-breaking
Q Du, Y Tao, X Tian
Journal of Elasticity 132 (2), 197-218, 2018
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 (6), 1363-1380, 2016
Robust discretization of nonlocal models related to peridynamics
Q Du, X Tian
Meshfree methods for partial differential equations VII, 97-113, 2015
Asymptotically compatible schemes for peridynamics based on numerical quadratures
Q Du, X Tian
ASME 2014 International Mechanical Engineering Congress and Exposition …, 2014
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
Mathematics of Smoothed Particle Hydrodynamics: A Study via Nonlocal Stokes Equations
Q Du, X Tian
Foundations of Computational Mathematics, 1-26, 2019
Nonlocal models with a finite range of nonlocal interactions
X Tian
Columbia University, 2017
A class of high order nonlocal operators
X Tian, Q Du
Archive for Rational Mechanics and Analysis 222 (3), 1521-1553, 2016
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
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
Nonlocal criteria for compactness in the space of vector fields
Q Du, T Mengesha, X Tian
arXiv preprint arXiv:1801.08000, 2018
Heterogeneously localized nonlocal operators, boundary traces and variational problems
Proceedings of the International Congress of Chinese Mathematicians …, 2018
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
Super-convergence of reproducing kernel approximation
Y Leng, X Tian, JT Foster
Computer Methods in Applied Mechanics and Engineering 352, 488--507, 2019
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