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
Du, Qiang; Tao, Yunzhe; Tian, Xiaochuan; Yang, Jiang Asymptotically compatible discretization of multidimensional nonlocal diffusion models and approximation of nonlocal Green’s functions. (English) Zbl 1466.65222 IMA J. Numer. Anal. 39, No. 2, 607-625 (2019). MSC: 65N80 65N35 65N06 PDFBibTeX XMLCite \textit{Q. Du} et al., IMA J. Numer. Anal. 39, No. 2, 607--625 (2019; Zbl 1466.65222) Full Text: DOI
Du, Qiang; Ju, Lili; Lu, Jianfang Analysis of fully discrete approximations for dissipative systems and application to time-dependent nonlocal diffusion problems. (English) Zbl 1419.65058 J. Sci. Comput. 78, No. 3, 1438-1466 (2019). MSC: 65M60 65R20 65L06 65L07 45A05 65M15 65M12 PDFBibTeX XMLCite \textit{Q. Du} et al., J. Sci. Comput. 78, No. 3, 1438--1466 (2019; Zbl 1419.65058) Full Text: DOI
Du, Qiang; Ju, Lili; Li, Xiao; Qiao, Zhonghua Maximum principle preserving exponential time differencing schemes for the nonlocal Allen-Cahn equation. (English) Zbl 1419.65018 SIAM J. Numer. Anal. 57, No. 2, 875-898 (2019). Reviewer: Victor Michel-Dansac (Toulouse) MSC: 65M06 65M12 65M15 65R20 35Q99 PDFBibTeX XMLCite \textit{Q. Du} et al., SIAM J. Numer. Anal. 57, No. 2, 875--898 (2019; Zbl 1419.65018) Full Text: DOI arXiv
Du, Qiang; Ju, Lili; Lu, Jianfang A discontinuous Galerkin method for one-dimensional time-dependent nonlocal diffusion problems. (English) Zbl 1405.65118 Math. Comput. 88, No. 315, 123-147 (2019). Reviewer: Elena V. Tabarintseva (Chelyabinsk) MSC: 65M60 45K05 35R09 PDFBibTeX XMLCite \textit{Q. Du} et al., Math. Comput. 88, No. 315, 123--147 (2019; Zbl 1405.65118) Full Text: DOI
Du, Qiang An invitation to nonlocal modeling, analysis and computation. (English) Zbl 1462.45019 Sirakov, Boyan (ed.) et al., Proceedings of the international congress of mathematicians 2018, ICM 2018, Rio de Janeiro, Brazil, August 1–9, 2018. Volume IV. Invited lectures. Hackensack, NJ: World Scientific; Rio de Janeiro: Sociedade Brasileira de Matemática (SBM). 3541-3569 (2018). MSC: 45P05 65R20 35R09 47G10 74G15 PDFBibTeX XMLCite \textit{Q. Du}, in: Proceedings of the international congress of mathematicians 2018, ICM 2018, Rio de Janeiro, Brazil, August 1--9, 2018. Volume IV. Invited lectures. Hackensack, NJ: World Scientific; Rio de Janeiro: Sociedade Brasileira de Matemática (SBM). 3541--3569 (2018; Zbl 1462.45019) Full Text: DOI
Sun, Qi; Du, Qiang; Ming, Ju Asymptotically compatible schemes for stochastic homogenization. (English) Zbl 1452.35022 SIAM J. Numer. Anal. 56, No. 3, 1942-1960 (2018); erratum ibid. 56, No. 4, 2698-2699 (2018). MSC: 35B27 65N30 PDFBibTeX XMLCite \textit{Q. Sun} et al., SIAM J. Numer. Anal. 56, No. 3, 1942--1960 (2018; Zbl 1452.35022) Full Text: DOI
Chen, An; Du, Qiang; Li, Changpin; Zhou, Zhi Asymptotically compatible schemes for space-time nonlocal diffusion equations. (English) Zbl 1422.65279 Chaos Solitons Fractals 102, 361-371 (2017). MSC: 65M70 65M06 65M12 35R10 PDFBibTeX XMLCite \textit{A. Chen} et al., Chaos Solitons Fractals 102, 361--371 (2017; Zbl 1422.65279) Full Text: DOI
Du, Qiang; Tao, Yunzhe; Tian, Xiaochuan; Yang, Jiang Robust a posteriori stress analysis for quadrature collocation approximations of nonlocal models via nonlocal gradients. (English) Zbl 1439.74011 Comput. Methods Appl. Mech. Eng. 310, 605-627 (2016). MSC: 74A10 74A20 PDFBibTeX XMLCite \textit{Q. Du} et al., Comput. Methods Appl. Mech. Eng. 310, 605--627 (2016; Zbl 1439.74011) Full Text: DOI
Du, Qiang; Tian, Xiaochuan Robust discretization of nonlocal models related to peridynamics. (English) Zbl 1342.74178 Griebel, Michael (ed.) et al., Meshfree methods for partial differential equations VII. Selected contributions based on the presentations at the 7th international workshop, Bonn, Germany, September 9–11, 2013. Cham: Springer (ISBN 978-3-319-06897-8/hbk; 978-3-319-06898-5/ebook). Lecture Notes in Computational Science and Engineering 100, 97-113 (2015). MSC: 74S30 74S05 74S20 37N15 74P15 PDFBibTeX XMLCite \textit{Q. Du} and \textit{X. Tian}, Lect. Notes Comput. Sci. Eng. 100, 97--113 (2015; Zbl 1342.74178) Full Text: DOI