Shen, Jie; Xu, Jie; Yang, Jiang A new class of efficient and robust energy stable schemes for gradient flows. (English) Zbl 1422.65080 SIAM Rev. 61, No. 3, 474-506 (2019). MSC: 65J08 35K20 35K35 35K55 65Z05 35Q35 PDFBibTeX XMLCite \textit{J. Shen} et al., SIAM Rev. 61, No. 3, 474--506 (2019; Zbl 1422.65080) Full Text: DOI arXiv
Shen, Jie; Xu, Jie Stabilized predictor-corrector schemes for gradient flows with strong anisotropic free energy. (English) Zbl 1475.82027 Commun. Comput. Phys. 24, No. 3, 635-654 (2018). MSC: 82M20 65M06 65M12 PDFBibTeX XMLCite \textit{J. Shen} and \textit{J. Xu}, Commun. Comput. Phys. 24, No. 3, 635--654 (2018; Zbl 1475.82027) Full Text: DOI
Cai, Yongyong; Shen, Jie Error estimates for a fully discretized scheme to a Cahn-Hilliard phase-field model for two-phase incompressible flows. (English) Zbl 1390.35225 Math. Comput. 87, No. 313, 2057-2090 (2018). MSC: 35Q30 65M12 65M60 PDFBibTeX XMLCite \textit{Y. Cai} and \textit{J. Shen}, Math. Comput. 87, No. 313, 2057--2090 (2018; Zbl 1390.35225) Full Text: DOI
Shen, Jie; Xu, Jie; Yang, Jiang The scalar auxiliary variable (SAV) approach for gradient flows. (English) Zbl 1380.65181 J. Comput. Phys. 353, 407-416 (2018). MSC: 65M06 35Q35 PDFBibTeX XMLCite \textit{J. Shen} et al., J. Comput. Phys. 353, 407--416 (2018; Zbl 1380.65181) Full Text: DOI
Shen, Jie; Yang, Xiaofeng; Yu, Haijun Efficient energy stable numerical schemes for a phase field moving contact line model. (English) Zbl 1351.76184 J. Comput. Phys. 284, 617-630 (2015). MSC: 76M20 65M06 65M60 76D05 82C26 82C80 PDFBibTeX XMLCite \textit{J. Shen} et al., J. Comput. Phys. 284, 617--630 (2015; Zbl 1351.76184) Full Text: DOI
Liu, Fei; Shen, Jie Stabilized semi-implicit spectral deferred correction methods for Allen-Cahn and Cahn-Hilliard equations. (English) Zbl 1335.65078 Math. Methods Appl. Sci. 38, No. 18, 4564-4575 (2015). MSC: 65M20 65M70 65M60 35Q35 PDFBibTeX XMLCite \textit{F. Liu} and \textit{J. Shen}, Math. Methods Appl. Sci. 38, No. 18, 4564--4575 (2015; Zbl 1335.65078) Full Text: DOI
Dong, S.; Shen, J. A time-stepping scheme involving constant coefficient matrices for phase-field simulations of two-phase incompressible flows with large density ratios. (English) Zbl 1277.76118 J. Comput. Phys. 231, No. 17, 5788-5804 (2012). MSC: 76T99 35Q35 76M22 PDFBibTeX XMLCite \textit{S. Dong} and \textit{J. Shen}, J. Comput. Phys. 231, No. 17, 5788--5804 (2012; Zbl 1277.76118) Full Text: DOI
Shen, Jie; Yang, Xiaofeng Numerical approximations of Allen-Cahn and Cahn-Hilliard equations. (English) Zbl 1201.65184 Discrete Contin. Dyn. Syst. 28, No. 4, 1669-1691 (2010). Reviewer: Wilhelm Heinrichs (Essen) MSC: 65M70 65M15 35Q35 65M12 65M20 65M60 PDFBibTeX XMLCite \textit{J. Shen} and \textit{X. Yang}, Discrete Contin. Dyn. Syst. 28, No. 4, 1669--1691 (2010; Zbl 1201.65184) Full Text: DOI Link
Feng, James J.; Liu, Chun; Shen, Jie; Yue, Pengtao An energetic variational formulation with phase field methods for interfacial dynamics of complex fluids: advantages and challenges. (English) Zbl 1181.76019 Calderer, Maria-Carme T. (ed.) et al., Modeling of soft matter. Selected papers based on the presentation at the workshop, Minneapolis, MN, USA, September 27–October 1, 2004. New York, NY: Springer (ISBN 0-387-29167-9/hbk). The IMA Volumes in Mathematics and its Applications 141, 1-26 (2005). MSC: 76A02 76M30 82D15 PDFBibTeX XMLCite \textit{J. J. Feng} et al., IMA Vol. Math. Appl. 141, 1--26 (2005; Zbl 1181.76019) Full Text: DOI
Liu, Chun; Shen, Jie A phase field model for the mixture of two incompressible fluids and its approximation by a Fourier-spectral method. (English) Zbl 1092.76069 Physica D 179, No. 3-4, 211-228 (2003). MSC: 76T99 PDFBibTeX XMLCite \textit{C. Liu} and \textit{J. Shen}, Physica D 179, No. 3--4, 211--228 (2003; Zbl 1092.76069) Full Text: DOI