Xiaochuan Tian

According to our database1, Xiaochuan Tian authored at least 20 papers between 2013 and 2021.

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Bibliography

2021
Asymptotically Compatible Reproducing Kernel Collocation and Meshfree Integration for Nonlocal Diffusion.
SIAM J. Numer. Anal., 2021

A Petrov-Galerkin method for nonlocal convection-dominated diffusion problems.
CoRR, 2021

An asymptotically compatible probabilistic collocation method for randomly heterogeneous nonlocal problems.
CoRR, 2021

The double adaptivity paradigm: (How to circumvent the discrete inf-sup conditions of Babuška and Brezzi).
Comput. Math. Appl., 2021

2020
A Physically Consistent, Flexible, and Efficient Strategy to Convert Local Boundary Conditions into Nonlocal Volume Constraints.
SIAM J. Sci. Comput., 2020

Asymptotically Compatible Schemes for Robust Discretization of Parametrized Problems with Applications to Nonlocal Models.
SIAM Rev., 2020

Mathematics of Smoothed Particle Hydrodynamics: A Study via Nonlocal Stokes Equations.
Found. Comput. Math., 2020

Asymptotically compatible reproducing kernel collocation and meshfree integration for the peridynamic Navier equation.
CoRR, 2020

Numerical methods for nonlocal and fractional models.
Acta Numer., 2020

Multiscale modeling, homogenization and nonlocal effects: Mathematical and computational issues.
Proceedings of the 75 Years of Mathematics of Computation, 2020

2019
Nonlocal Models with Heterogeneous Localization and Their Application to Seamless Local-Nonlocal Coupling.
Multiscale Model. Simul., 2019

Multiscale Modeling, Homogenization and Nonlocal Effects: Mathematical and Computational Issues.
CoRR, 2019

2018
A Quasi-nonlocal Coupling Method for Nonlocal and Local Diffusion Models.
SIAM J. Numer. Anal., 2018

Stability of Nonlocal Dirichlet Integrals and Implications for Peridynamic Correspondence Material Modeling.
SIAM J. Appl. Math., 2018

2017
Trace Theorems for some Nonlocal Function Spaces with Heterogeneous Localization.
SIAM J. Math. Anal., 2017

Nonlocal diffusion and peridynamic models with Neumann type constraints and their numerical approximations.
Appl. Math. Comput., 2017

2016
Asymptotically compatible schemes for the approximation of fractional Laplacian and related nonlocal diffusion problems on bounded domains.
Adv. Comput. Math., 2016

2015
Nonconforming Discontinuous Galerkin Methods for Nonlocal Variational Problems.
SIAM J. Numer. Anal., 2015

2014
Asymptotically Compatible Schemes and Applications to Robust Discretization of Nonlocal Models.
SIAM J. Numer. Anal., 2014

2013
Analysis and Comparison of Different Approximations to Nonlocal Diffusion and Linear Peridynamic Equations.
SIAM J. Numer. Anal., 2013


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