Xiaochuan Tian

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All published works

Action	Title	Year	Authors
+	Asymptotically compatible schemes for nonlinear variational models via Gamma-convergence and applications to nonlocal problems	2024	Qiang Du James Scott Xiaochuan Tian
+	Compactness results for a Dirichlet energy of nonlocal gradient with applications	2024	Zhaolong Han Tadele Mengesha Xiaochuan Tian
+ PDF Chat	Numerical analysis of a class of penalty discontinuous Galerkin methods for nonlocal diffusion problems	2024	Qiang Du Lili Ju Jianfang Lu Xiaochuan Tian
+	Numerical analysis of a class of penalty discontinuous Galerkin methods for nonlocal diffusion problems	2024	Qiang Du Lili Ju Jianfang Lu Xiaochuan Tian
+ PDF Chat	A Fast and Accurate Solver for the Fractional Fokker-Planck Equation with Dirac-Delta Initial Conditions	2024	Q. Ye Xiaochuan Tian Dong Wang
+ PDF Chat	Compactness results for a Dirichlet energy of nonlocal gradient with applications	2024	Zhaolong Han Tadele Mengesha Xiaochuan Tian
+ PDF Chat	Asymptotically compatible schemes for nonlinear variational models via Gamma-convergence and applications to nonlocal problems	2024	Qiang Du James M. Scott Xiaochuan Tian
+ PDF Chat	Correction to: Monotone Meshfree Methods for Linear Elliptic Equations in Non-divergence Form via Nonlocal Relaxation	2023	Qihao Ye Xiaochuan Tian
+ PDF Chat	Nonlocal half-ball vector operators on bounded domains: Poincaré inequality and its applications	2023	Zhaolong Han Xiaochuan Tian
+ PDF Chat	Monotone Meshfree Methods for Linear Elliptic Equations in Non-divergence Form via Nonlocal Relaxation	2023	Qihao Ye Xiaochuan Tian
+ PDF Chat	Nonlocal Diffusion Models with Consistent Local and Fractional Limits	2023	Qiang Du Xiaochuan Tian Zhi Zhou
+	$ L^{p} $ compactness criteria with an application to variational convergence of some nonlocal energy functionals	2023	Qiang Du Tadele Mengesha Xiaochuan Tian
+	A neural network kernel decomposition for learning multiple steady states in parameterized dynamical systems	2023	Yimeng Zhang Alexander Cloninger Bo Hu Li Xiaochuan Tian
+	Gaussian radial basis functions collocation for fractional PDEs: methodology and error analysis	2023	Xiaochuan Tian Yixuan Wu Yanzhi Zhang
+ PDF Chat	A meshfree peridynamic model for brittle fracture in randomly heterogeneous materials	2022	Yi‐Ming Fan Huaiqian You Xiaochuan Tian Yang Xiu Xingjie Li Naveen Prakash Yue Yu
+ PDF Chat	An asymptotically compatible probabilistic collocation method for randomly heterogeneous nonlocal problems	2022	Yiming Fan Xiaochuan Tian Xiu Yang Xingjie Li Clayton Webster Yue Yu
+ PDF Chat	Efficient optimization-based quadrature for variational discretization of nonlocal problems	2022	Marco Pasetto Zhaoxiang Shen Marta D’Elia Xiaochuan Tian Nathaniel Trask David Kamensky
+ PDF Chat	Nonlocal trace spaces and extension results for nonlocal calculus	2022	Qiang Du Xiaochuan Tian Cory Wright Yue Yu
+ PDF Chat	Fractional Hardy-type and trace theorems for nonlocal function spaces with heterogeneous localization	2022	Qiang Du Tadele Mengesha Xiaochuan Tian
+ PDF Chat	A Petrov-Galerkin method for nonlocal convection-dominated diffusion problems	2022	Yu Leng Xiaochuan Tian Leszek Demkowicz Héctor Gómez John T. Foster
+	Nonlocal diffusion models with consistent local and fractional limits	2022	Qiang Du Xiaochuan Tian Zhi Zhou
+	A Meshfree Peridynamic Model for Brittle Fracture in Randomly Heterogeneous Materials	2022	Yi‐Ming Fan Huaiqian You Xiaochuan Tian Yang Xiu Xingjie Li Naveen Prakash Yue Yu
+	Monotone meshfree methods for linear elliptic equations in non-divergence form via nonlocal relaxation	2022	Qihao Ye Xiaochuan Tian
+	Nonlocal half-ball vector operators on bounded domains: Poincaré inequality and its applications	2022	Zhaolong Han Xiaochuan Tian
+	A Review of Local-to-Nonlocal Coupling Methods in Nonlocal Diffusion and Nonlocal Mechanics	2021	Marta D’Elia Xingjie Li Pablo Seleson Xiaochuan Tian Yue Yu
+	Asymptotically Compatible Reproducing Kernel Collocation and Meshfree Integration for Nonlocal Diffusion	2021	Yu Leng Xiaochuan Tian Nathaniel Trask John T. Foster
+	Fractional Hardy-type and trace theorems for nonlocal function spaces with heterogeneous localization	2021	Qiang Du Tadele Mengesha Xiaochuan Tian
+	Nonlocal Trace Spaces and Extension Results for Nonlocal Calculus	2021	Qiang Du Xiaochuan Tian Cory Wright Yue Yu
+ PDF Chat	The double adaptivity paradigm	2020	Leszek Demkowicz Thomas Führer Norbert Heuer Xiaochuan Tian
+ PDF Chat	Asymptotically compatible reproducing kernel collocation and meshfree integration for the peridynamic Navier equation	2020	Yu Leng Xiaochuan Tian Nathaniel Trask John T. Foster
+ PDF Chat	Numerical methods for nonlocal and fractional models	2020	Marta D’Elia Qiang Du Christian Glusa Max Gunzburger Xiaochuan Tian Zhi Zhou
+	Numerical methods for nonlocal and fractional models	2020	Marta D’Elia Qiang Du Christian Glusa Max Gunzburger Xiaochuan Tian Zhi Zhou
+ PDF Chat	A Physically Consistent, Flexible, and Efficient Strategy to Convert Local Boundary Conditions into Nonlocal Volume Constraints	2020	Marta D’Elia Xiaochuan Tian Yue Yu
+ PDF Chat	Multiscale modeling, homogenization and nonlocal effects: Mathematical and computational issues	2020	Qiang Du Björn Engquist Xiaochuan Tian
+ PDF Chat	Mathematics of Smoothed Particle Hydrodynamics: A Study via Nonlocal Stokes Equations	2019	Qiang Du Xiaochuan Tian
+	A Discontinuous Galerkin Method with Penalty for One-Dimensional Nonlocal Diffusion Problems	2019	Qiang Du Lili Ju Jianfang Lu Xiaochuan Tian
+	A physically-consistent, flexible and efficient strategy to convert local boundary conditions into nonlocal volume constraints	2019	Marta D’Elia Xiaochuan Tian Yue Yu
+	Asymptotically compatible reproducing kernel collocation and meshfree integration for nonlocal diffusion	2019	Yu Leng Xiaochuan Tian Nathaniel Trask John T. Foster
+	Multiscale Modeling, Homogenization and Nonlocal Effects: Mathematical and Computational Issues	2019	Qiang Du Björn Engquist Xiaochuan Tian
+	A review of Local-to-Nonlocal coupling methods in nonlocal diffusion and nonlocal mechanics	2019	Marta D’Elia Xingjie Li Pablo Seleson Xiaochuan Tian Yue Yu
+ PDF Chat	Fast algorithm for computing nonlocal operators with finite interaction distance	2019	Xiaochuan Tian Björn Engquist
+	Mathematics of Smoothed Particle Hydrodynamics, Part I: a Nonlocal Stokes Equation	2018	Qiang Du Xiaochuan Tian
+	Asymptotically compatible discretization of multidimensional nonlocal diffusion models and approximation of nonlocal Green’s functions	2018	Qiang Du Yunzhe Tao Xiaochuan Tian Jiang Yang
+ PDF Chat	A Quasi-nonlocal Coupling Method for Nonlocal and Local Diffusion Models	2018	Qiang Du Xingjie Helen Li Jianfeng Lu Xiaochuan Tian
+	$L^{p}$ compactness criteria with an application to variational convergence of some nonlocal energy functionals	2018	Qiang Du Tadele Mengesha Xiaochuan Tian
+	Mathematics of Smoothed Particle Hydrodynamics: a Study via Nonlocal Stokes Equations	2018	Qiang Du Xiaochuan Tian
+ PDF Chat	Stability of Nonlocal Dirichlet Integrals and Implications for Peridynamic Correspondence Material Modeling	2018	Qiang Du Xiaochuan Tian
+	Trace Theorems for some Nonlocal Function Spaces with Heterogeneous Localization	2017	Xiaochuan Tian Qiang Du
+	Nonlocal models with a finite range of nonlocal interactions	2017	Xiaochuan Tian
+	Stability of nonlocal Dirichlet integrals and implications for peridynamic correspondence material modeling	2017	Qiang Du Xiaochuan Tian
+	A quasinonlocal coupling method for nonlocal and local diffusion models	2017	Qiang Du Xingjie Helen Li Jianfeng Lu Xiaochuan Tian
+	Asymptotically compatible schemes for the approximation of fractional Laplacian and related nonlocal diffusion problems on bounded domains	2016	Xiaochuan Tian Qiang Du Max Gunzburger
+	A Class of High Order Nonlocal Operators	2016	Xiaochuan Tian Qiang Du
+	Nonconforming Discontinuous Galerkin Methods for Nonlocal Variational Problems	2015	Xiaochuan Tian Qiang Du
+	Analysis and Comparison of Different Approximations to Nonlocal Diffusion and Linear Peridynamic Equations	2013	Xiaochuan Tian Qiang Du

Common Coauthors

Coauthor	Papers Together
Qiang Du	30
Marta D’Elia	7
Tadele Mengesha	6
Zhi Zhou	4
Xingjie Li	4
Yu Leng	4
Nathaniel Trask	4
John T. Foster	4
Björn Engquist	3
Qihao Ye	3
Lili Ju	3
Yue Yu	3
Max Gunzburger	3
Zhaolong Han	3
Jianfang Lu	3
Jianfeng Lu	2
Leszek Demkowicz	2
Yue Yu	2
Yi‐Ming Fan	2
Xingjie Helen Li	2
Huaiqian You	2
Yang Xiu	2
Pablo Seleson	2
Yue Yu	2
Christian Glusa	2
Yiming Fan	1
Naveen Prakash	1
Marco Pasetto	1
Cory Wright	1
James M. Scott	1
Norbert Heuer	1
Yunzhe Tao	1
Clayton Webster	1
James Scott	1
Thomas Führer	1
Bo Hu Li	1
Cory Wright	1
David Kamensky	1
Q. Ye	1
Zhaolong Han	1
Yanzhi Zhang	1
Alexander Cloninger	1
Héctor Gómez	1
Zhaoxiang Shen	1
Naveen Prakash	1
Xiu Yang	1
Yue Yu	1
Yue Yu	1
Dong Wang	1
Xingjie Li	1

Commonly Cited References

Action	Title	Year	Authors	# of times referenced
+	Analysis and Approximation of Nonlocal Diffusion Problems with Volume Constraints	2012	Qiang Du Max Gunzburger Richard B. Lehoucq Kun Zhou	28
+	Analysis and Comparison of Different Approximations to Nonlocal Diffusion and Linear Peridynamic Equations	2013	Xiaochuan Tian Qiang Du	17
+	The random walk's guide to anomalous diffusion: a fractional dynamics approach	2000	Ralf Metzler J. Klafter	14
+ PDF Chat	Image Recovery via Nonlocal Operators	2009	Yifei Lou Xiaoqun Zhang Stanley Osher Andrea L. Bertozzi	13
+	Nonlocal Operators with Applications to Image Processing	2008	Guy Gilboa Stanley Osher	12
+	Analysis of a scalar nonlocal peridynamic model with a sign changing kernel	2013	Tadele Mengesha Qiang Du	11
+	Nonconforming Discontinuous Galerkin Methods for Nonlocal Variational Problems	2015	Xiaochuan Tian Qiang Du	11
+ PDF Chat	Nonlocal Diffusion Problems	2010	Fuensanta Andreu-Vaillo José M. Mazón Julio D. Rossi J. Julián Toledo-Melero	11
+	Trace Theorems for some Nonlocal Function Spaces with Heterogeneous Localization	2017	Xiaochuan Tian Qiang Du	10
+ PDF Chat	An estimate in the spirit of Poincaré's inequality	2004	Augusto C. Ponce	10
+	Nonlocal Modeling, Analysis, and Computation	2019	Qiang Du	10
+	An asymptotically compatible meshfree quadrature rule for nonlocal problems with applications to peridynamics	2018	Nathaniel Trask Huaiqian You Yue Yu Michael L. Parks	9
+	A Nonlocal Vector Calculus with Application to Nonlocal Boundary Value Problems	2010	Max Gunzburger Richard B. Lehoucq	9
+	None	1999	Peter W. Bates Adam Chmaj	8
+	Nonlocal Convection-Diffusion Problems on Bounded Domains and Finite-Range Jump Processes	2017	Marta D’Elia Qiang Du Max Gunzburger Richard B. Lehoucq	8
+	Nonlocal Linear Image Regularization and Supervised Segmentation	2007	Guy Gilboa Stanley Osher	8
+	Asymptotically Compatible Fourier Spectral Approximations of Nonlocal Allen--Cahn Equations	2016	Qiang Du Jiang Yang	7
+ PDF Chat	The Dirichlet problem for nonlocal operators	2014	Matthieu Felsinger Moritz Kaßmann P. W. Voigt	7
+ PDF Chat	Mathematics of Smoothed Particle Hydrodynamics: A Study via Nonlocal Stokes Equations	2019	Qiang Du Xiaochuan Tian	7
+ PDF Chat	Another look at Sobolev spaces	2001	Jean Bourgain Haı̈m Brezis Petru Mironescu	7
+ PDF Chat	A conservative nonlocal convection–diffusion model and asymptotically compatible finite difference discretization	2017	Hao Tian Lili Ju Qiang Du	7
+	The exit-time problem for a Markov jump process	2014	Nathanial Burch Marta D’Elia Richard B. Lehoucq	6
+	Hitchhikerʼs guide to the fractional Sobolev spaces	2011	Eleonora Di Nezza Giampiero Palatucci Enrico Valdinoci	6
+	NONLOCAL KORN-TYPE CHARACTERIZATION OF SOBOLEV VECTOR FIELDS	2012	Tadele Mengesha	6
+ PDF Chat	Nonlocal elliptic equations in bounded domains: a survey	2015	Xavier Ros‐Oton	6
+ PDF Chat	Analysis of a nonlocal-in-time parabolic equation	2016	Qiang Du Jiang Yang Zhi Zhou	5
+ PDF Chat	An asymptotically compatible formulation for local-to-nonlocal coupling problems without overlapping regions	2020	Huaiqian You Yue Yu David Kamensky	5
+ PDF Chat	Nonlocal gradient operators with a nonspherical interaction neighborhood and their applications	2019	Hwi Lee Qiang Du	5
+ PDF Chat	A Physically Consistent, Flexible, and Efficient Strategy to Convert Local Boundary Conditions into Nonlocal Volume Constraints	2020	Marta D’Elia Xiaochuan Tian Yue Yu	5
+ PDF Chat	Multiscaling fractional advection‐dispersion equations and their solutions	2003	R. Schumer David A. Benson Mark M. Meerschaert Boris Baeumer	5
+ PDF Chat	Application of a fractional advection‐dispersion equation	2000	David A. Benson Stephen W. Wheatcraft Mark M. Meerschaert	5
+	Nonlocal convection-diffusion volume-constrained problems and jump processes	2014	Qiang Du Zhan Huang Richard B. Lehoucq	5
+	An asymptotically compatible approach for Neumann-type boundary condition on nonlocal problems	2019	Huaiqian You Xinyang Lu Nathaniel Task Yue Yu	5
+ PDF Chat	Stability of Nonlocal Dirichlet Integrals and Implications for Peridynamic Correspondence Material Modeling	2018	Qiang Du Xiaochuan Tian	5
+	Asymptotically Compatible Reproducing Kernel Collocation and Meshfree Integration for Nonlocal Diffusion	2021	Yu Leng Xiaochuan Tian Nathaniel Trask John T. Foster	5
+	Stochastic Models for Fractional Calculus	2019	Mark M. Meerschaert Alla Sikorskii	5
+ PDF Chat	Nonlocal Diffusion and Applications	2016	Claudia Bucur Enrico Valdinoci	4
+	Function spaces and extension results for nonlocal Dirichlet problems	2018	Bartłomiej Dyda Moritz Kaßmann	4
+ PDF Chat	Numerical methods for nonlocal and fractional models	2020	Marta D’Elia Qiang Du Christian Glusa Max Gunzburger Xiaochuan Tian Zhi Zhou	4
+ PDF Chat	A PDE Approach to Fractional Diffusion in General Domains: A Priori Error Analysis	2014	Ricardo H. Nochetto Enrique Otárola Abner J. Salgado	4
+ PDF Chat	The restaurant at the end of the random walk: recent developments in the description of anomalous transport by fractional dynamics	2004	Ralf Metzler J. Klafter	4
+	Asymptotically compatible schemes for the approximation of fractional Laplacian and related nonlocal diffusion problems on bounded domains	2016	Xiaochuan Tian Qiang Du Max Gunzburger	4
+	CLASSICAL, NONLOCAL, AND FRACTIONAL DIFFUSION EQUATIONS ON BOUNDED DOMAINS	2011	Nathanial Burch Richard B. Lehoucq	4
+	The fractional Laplacian operator on bounded domains as a special case of the nonlocal diffusion operator	2013	Marta D’Elia Max Gunzburger	4
+	Eulerian derivation of the fractional advection–dispersion equation	2001	R. Schumer David A. Benson Mark M. Meerschaert Stephen W. Wheatcraft	4
+	A discontinuous Galerkin method for one-dimensional time-dependent nonlocal diffusion problems	2017	Qiang Du Lili Ju Jianfang Lu	4
+ PDF Chat	Critical thresholds in flocking hydrodynamics with non-local alignment	2014	Eitan Tadmor Changhui Tan	4
+	Nonlocal models with a finite range of nonlocal interactions	2017	Xiaochuan Tian	4
+	Localization of nonlocal gradients in various topologies	2014	Tadele Mengesha Daniel Spector	4
+	Functional Analysis, Sobolev Spaces and Partial Differential Equations	2010	Haı̈m Brezis	4