Ye, Qihao; Tian, Xiaochuan Correction to: “Monotone meshfree methods for linear elliptic equations in non-divergence form via nonlocal relaxation”. (English) Zbl 1525.65116 J. Sci. Comput. 97, No. 2, Paper No. 46, 1 p. (2023). MSC: 65N06 65N12 65K10 35B50 35J15 65R20 35J70 45A05 PDFBibTeX XMLCite \textit{Q. Ye} and \textit{X. Tian}, J. Sci. Comput. 97, No. 2, Paper No. 46, 1 p. (2023; Zbl 1525.65116) Full Text: DOI
Ye, Qihao; Tian, Xiaochuan Monotone meshfree methods for linear elliptic equations in non-divergence form via nonlocal relaxation. (English) Zbl 1522.65188 J. Sci. Comput. 96, No. 3, Paper No. 85, 33 p. (2023); correction ibid. 97, No. 2, Paper No. 46, 1 p. (2023). MSC: 65N06 65N12 65K10 35B50 35J15 65R20 35J70 45A05 PDFBibTeX XMLCite \textit{Q. Ye} and \textit{X. Tian}, J. Sci. Comput. 96, No. 3, Paper No. 85, 33 p. (2023; Zbl 1522.65188) Full Text: DOI arXiv
Leng, Yu; Tian, Xiaochuan; Trask, Nathaniel; Foster, John T. Asymptotically compatible reproducing kernel collocation and meshfree integration for nonlocal diffusion. (English) Zbl 1456.82636 SIAM J. Numer. Anal. 59, No. 1, 88-118 (2021). MSC: 82C21 65R20 65M70 65M12 46N20 45A05 PDFBibTeX XMLCite \textit{Y. Leng} et al., SIAM J. Numer. Anal. 59, No. 1, 88--118 (2021; Zbl 1456.82636) Full Text: DOI arXiv
D’Elia, Marta; Tian, Xiaochuan; Yu, Yue A physically consistent, flexible, and efficient strategy to convert local boundary conditions into nonlocal volume constraints. (English) Zbl 1474.45073 SIAM J. Sci. Comput. 42, No. 4, A1935-A1949 (2020). MSC: 45L05 65R20 PDFBibTeX XMLCite \textit{M. D'Elia} et al., SIAM J. Sci. Comput. 42, No. 4, A1935--A1949 (2020; Zbl 1474.45073) Full Text: DOI arXiv
Tian, Xiaochuan; Du, Qiang Asymptotically compatible schemes for robust discretization of parametrized problems with applications to nonlocal models. (English) Zbl 1485.65058 SIAM Rev. 62, No. 1, 199-227 (2020). MSC: 65J10 49M25 65N30 65R20 82C21 46N40 45A05 PDFBibTeX XMLCite \textit{X. Tian} and \textit{Q. Du}, SIAM Rev. 62, No. 1, 199--227 (2020; Zbl 1485.65058) Full Text: DOI
Du, Qiang; Ju, Lili; Lu, Jianfang; Tian, Xiaochuan A discontinuous Galerkin method with penalty for one-dimensional nonlocal diffusion problems. (English) Zbl 1449.65242 Commun. Appl. Math. Comput. 2, No. 1, 31-55 (2020). MSC: 65M60 65R20 45A05 PDFBibTeX XMLCite \textit{Q. Du} et al., Commun. Appl. Math. Comput. 2, No. 1, 31--55 (2020; Zbl 1449.65242) Full Text: DOI
Tao, Yunzhe; Tian, Xiaochuan; Du, Qiang Nonlocal models with heterogeneous localization and their application to seamless local-nonlocal coupling. (English) Zbl 1447.45001 Multiscale Model. Simul. 17, No. 3, 1052-1075 (2019). MSC: 45A05 45K05 47G10 74G65 74H20 74H25 PDFBibTeX XMLCite \textit{Y. Tao} et al., Multiscale Model. Simul. 17, No. 3, 1052--1075 (2019; Zbl 1447.45001) Full Text: DOI
Tian, Xiaochuan; Engquist, Björn Fast algorithm for computing nonlocal operators with finite interaction distance. (English) Zbl 1428.82083 Commun. Math. Sci. 17, No. 6, 1653-1670 (2019). MSC: 82M99 65R20 82C21 65F05 45K05 PDFBibTeX XMLCite \textit{X. Tian} and \textit{B. Engquist}, Commun. Math. Sci. 17, No. 6, 1653--1670 (2019; Zbl 1428.82083) Full Text: DOI arXiv
Du, Qiang; Tao, Yunzhe; Tian, Xiaochuan A peridynamic model of fracture mechanics with bond-breaking. (English) Zbl 1395.74041 J. Elasticity 132, No. 2, 197-218 (2018). MSC: 74H20 74H25 45K05 47G10 74R10 PDFBibTeX XMLCite \textit{Q. Du} et al., J. Elasticity 132, No. 2, 197--218 (2018; Zbl 1395.74041) Full Text: DOI
Du, Qiang; Li, Xingjie Helen; Lu, Jianfeng; Tian, Xiaochuan A quasi-nonlocal coupling method for nonlocal and local diffusion models. (English) Zbl 06880667 SIAM J. Numer. Anal. 56, No. 3, 1386-1404 (2018). MSC: 65J10 49M25 65N30 65R20 82C21 46N40 45A05 PDFBibTeX XMLCite \textit{Q. Du} et al., SIAM J. Numer. Anal. 56, No. 3, 1386--1404 (2018; Zbl 06880667) Full Text: DOI arXiv
Du, Qiang; Tian, Xiaochuan Stability of nonlocal Dirichlet integrals and implications for peridynamic correspondence material modeling. (English) Zbl 1394.45002 SIAM J. Appl. Math. 78, No. 3, 1536-1552 (2018). Reviewer: Rodica Luca (Iaşi) MSC: 45A05 45K05 47G10 74G65 PDFBibTeX XMLCite \textit{Q. Du} and \textit{X. Tian}, SIAM J. Appl. Math. 78, No. 3, 1536--1552 (2018; Zbl 1394.45002) Full Text: DOI arXiv
Tao, Yunzhe; Tian, Xiaochuan; Du, Qiang Nonlocal diffusion and peridynamic models with Neumann type constraints and their numerical approximations. (English) Zbl 1411.74058 Appl. Math. Comput. 305, 282-298 (2017). MSC: 74S05 65N30 45K05 74A45 PDFBibTeX XMLCite \textit{Y. Tao} et al., Appl. Math. Comput. 305, 282--298 (2017; Zbl 1411.74058) Full Text: DOI
Tian, Xiaochuan; Du, Qiang Nonconforming discontinuous Galerkin methods for nonlocal variational problems. (English) Zbl 1322.65109 SIAM J. Numer. Anal. 53, No. 2, 762-781 (2015). MSC: 65N30 65R20 46N40 45A05 35J86 PDFBibTeX XMLCite \textit{X. Tian} and \textit{Q. Du}, SIAM J. Numer. Anal. 53, No. 2, 762--781 (2015; Zbl 1322.65109) Full Text: DOI
Tian, Xiaochuan; Du, Qiand Analysis and comparison of different approximations to nonlocal diffusion and linear peridynamic equations. (English) Zbl 1295.82021 SIAM J. Numer. Anal. 51, No. 6, 3458-3482 (2013). Reviewer: Pavel Burda (Praha) MSC: 82C21 65R20 65M60 46N20 45A05 65M06 82-08 PDFBibTeX XMLCite \textit{X. Tian} and \textit{Q. Du}, SIAM J. Numer. Anal. 51, No. 6, 3458--3482 (2013; Zbl 1295.82021) Full Text: DOI