Liu, Chun; Wang, Cheng; Wise, Steven M.; Yue, Xingye; Zhou, Shenggao A second order accurate, positivity preserving numerical method for the Poisson-Nernst-Planck system and its convergence analysis. (English) Zbl 07751604 J. Sci. Comput. 97, No. 1, Paper No. 23, 35 p. (2023). MSC: 65-XX 35K35 35K55 65M06 65M12 PDFBibTeX XMLCite \textit{C. Liu} et al., J. Sci. Comput. 97, No. 1, Paper No. 23, 35 p. (2023; Zbl 07751604) Full Text: DOI arXiv
Duan, Chenghua; Chen, Wenbin; Liu, Chun; Wang, Cheng; Zhou, Shenggao Convergence analysis of structure-preserving numerical methods for nonlinear Fokker-Planck equations with nonlocal interactions. (English) Zbl 07780620 Math. Methods Appl. Sci. 45, No. 7, 3764-3781 (2022). MSC: 65M75 65M06 65M12 65M15 35K65 76M20 76M28 35B40 35R60 35Q84 PDFBibTeX XMLCite \textit{C. Duan} et al., Math. Methods Appl. Sci. 45, No. 7, 3764--3781 (2022; Zbl 07780620) Full Text: DOI
Liu, Chun; Wang, Cheng; Wang, Yiwei A second-order accurate, operator splitting scheme for reaction-diffusion systems in an energetic variational formulation. (English) Zbl 07569639 SIAM J. Sci. Comput. 44, No. 4, A2276-A2301 (2022). MSC: 65-XX 35K35 35K55 49J40 65M06 65M12 PDFBibTeX XMLCite \textit{C. Liu} et al., SIAM J. Sci. Comput. 44, No. 4, A2276--A2301 (2022; Zbl 07569639) Full Text: DOI arXiv
Cheng, Qing; Delafrouz, Pourya; Liang, Jie; Liu, Chun; Shen, Jie Modeling and simulation of cell nuclear architecture reorganization process. (English) Zbl 07524801 J. Comput. Phys. 449, Article ID 110808, 19 p. (2022). MSC: 65Mxx 92Cxx 35Kxx PDFBibTeX XMLCite \textit{Q. Cheng} et al., J. Comput. Phys. 449, Article ID 110808, 19 p. (2022; Zbl 07524801) Full Text: DOI arXiv
Liu, Chun; Wang, Yiwei; Zhang, Teng-Fei Global existence of classical solutions for a reactive polymeric fluid near equilibrium. (English) Zbl 1506.35168 Calc. Var. Partial Differ. Equ. 61, No. 3, Paper No. 117, 37 p. (2022). MSC: 35Q35 35Q84 76A10 76V05 76M30 82D60 35A01 35A15 35B45 PDFBibTeX XMLCite \textit{C. Liu} et al., Calc. Var. Partial Differ. Equ. 61, No. 3, Paper No. 117, 37 p. (2022; Zbl 1506.35168) Full Text: DOI arXiv
Guo, Zhenlin; Cheng, Qing; Lin, Ping; Liu, Chun; Lowengrub, John Second order approximation for a quasi-incompressible Navier-Stokes Cahn-Hilliard system of two-phase flows with variable density. (English) Zbl 07516811 J. Comput. Phys. 448, Article ID 110727, 17 p. (2022). MSC: 76M20 65M06 76T06 PDFBibTeX XMLCite \textit{Z. Guo} et al., J. Comput. Phys. 448, Article ID 110727, 17 p. (2022; Zbl 07516811) Full Text: DOI
Liu, Chun; Wang, Cheng; Wang, Yiwei; Wise, Steven M. Convergence analysis of the variational operator splitting scheme for a reaction-diffusion system with detailed balance. (English) Zbl 07516278 SIAM J. Numer. Anal. 60, No. 2, 781-803 (2022). MSC: 65-XX 35K35 35K55 49J40 65M06 65M12 PDFBibTeX XMLCite \textit{C. Liu} et al., SIAM J. Numer. Anal. 60, No. 2, 781--803 (2022; Zbl 07516278) Full Text: DOI arXiv
Liu, Chun; Wang, Cheng; Wise, Steven M.; Yue, Xingye; Zhou, Shenggao An iteration solver for the Poisson-Nernst-Planck system and its convergence analysis. (English) Zbl 1503.65177 J. Comput. Appl. Math. 406, Article ID 114017, 13 p. (2022). MSC: 65M06 35K35 35K55 49J40 65M12 PDFBibTeX XMLCite \textit{C. Liu} et al., J. Comput. Appl. Math. 406, Article ID 114017, 13 p. (2022; Zbl 1503.65177) Full Text: DOI
Liu, Chun; Wang, Cheng; Wang, Yiwei A structure-preserving, operator splitting scheme for reaction-diffusion equations with detailed balance. (English) Zbl 07513840 J. Comput. Phys. 436, Article ID 110253, 22 p. (2021). MSC: 65Mxx 35Kxx 35Qxx PDFBibTeX XMLCite \textit{C. Liu} et al., J. Comput. Phys. 436, Article ID 110253, 22 p. (2021; Zbl 07513840) Full Text: DOI arXiv
Knopf, Patrik; Lam, Kei Fong; Liu, Chun; Metzger, Stefan Phase-field dynamics with transfer of materials: the Cahn-Hilliard equation with reaction rate dependent dynamic boundary conditions. (English) Zbl 1470.35173 ESAIM, Math. Model. Numer. Anal. 55, No. 1, 229-282 (2021). MSC: 35K35 35A01 35A02 35A35 35B40 35K58 65M60 65M12 PDFBibTeX XMLCite \textit{P. Knopf} et al., ESAIM, Math. Model. Numer. Anal. 55, No. 1, 229--282 (2021; Zbl 1470.35173) Full Text: DOI arXiv
Liu, Chun; Wang, Cheng; Wise, Steven M.; Yue, Xingye; Zhou, Shenggao A positivity-preserving, energy stable and convergent numerical scheme for the Poisson-Nernst-Planck system. (English) Zbl 1480.65213 Math. Comput. 90, No. 331, 2071-2106 (2021). MSC: 65M06 65M12 35C20 35K35 35K55 35A01 35B09 49J40 78A57 35Q60 PDFBibTeX XMLCite \textit{C. Liu} et al., Math. Comput. 90, No. 331, 2071--2106 (2021; Zbl 1480.65213) Full Text: DOI arXiv
Duan, Chenghua; Chen, Wenbin; Liu, Chun; Yue, Xingye; Zhou, Shenggao Structure-preserving numerical methods for nonlinear Fokker-Planck equations with nonlocal interactions by an energetic variational approach. (English) Zbl 1457.65046 SIAM J. Sci. Comput. 43, No. 1, B82-B107 (2021). Reviewer: Marius Ghergu (Dublin) MSC: 65M06 65M12 35K65 76S05 76M20 82C31 35A15 35Q84 35Q35 PDFBibTeX XMLCite \textit{C. Duan} et al., SIAM J. Sci. Comput. 43, No. 1, B82--B107 (2021; Zbl 1457.65046) Full Text: DOI arXiv
Yang, Ying; Tang, Ming; Liu, Chun; Lu, Benzhuo; Zhong, Liuqiang Superconvergent gradient recovery for nonlinear Poisson-Nernst-Planck equations with applications to the ion channel problem. (English) Zbl 1465.65148 Adv. Comput. Math. 46, No. 6, Paper No. 78, 34 p. (2020). MSC: 65N30 65N12 65N15 78A57 92C40 35Q60 PDFBibTeX XMLCite \textit{Y. Yang} et al., Adv. Comput. Math. 46, No. 6, Paper No. 78, 34 p. (2020; Zbl 1465.65148) Full Text: DOI
Liu, Chun; Wang, Yiwei A variational Lagrangian scheme for a phase-field model: a discrete energetic variational approach. (English) Zbl 1456.65118 SIAM J. Sci. Comput. 42, No. 6, B1541-B1569 (2020). Reviewer: Bülent Karasözen (Ankara) MSC: 65M60 65M50 35A15 PDFBibTeX XMLCite \textit{C. Liu} and \textit{Y. Wang}, SIAM J. Sci. Comput. 42, No. 6, B1541--B1569 (2020; Zbl 1456.65118) Full Text: DOI arXiv
Lu, Min-Jhe; Liu, Chun; Li, Shuwang Nonlinear simulation of an elastic tumor-host interface. (English) Zbl 1425.92115 Comput. Math. Biophys. 7, No. 1, 25-47 (2019). MSC: 92C50 35Q92 PDFBibTeX XMLCite \textit{M.-J. Lu} et al., Comput. Math. Biophys. 7, No. 1, 25--47 (2019; Zbl 1425.92115) Full Text: DOI arXiv
Jiang, Jie; Li, Yinghua; Liu, Chun Two-phase incompressible flows with variable density: an energetic variational approach. (English) Zbl 1361.35129 Discrete Contin. Dyn. Syst. 37, No. 6, 3243-3284 (2017). MSC: 35Q30 35Q35 76T99 35B40 35B32 35A15 35D30 35D35 PDFBibTeX XMLCite \textit{J. Jiang} et al., Discrete Contin. Dyn. Syst. 37, No. 6, 3243--3284 (2017; Zbl 1361.35129) Full Text: DOI
Metti, Maximilian S.; Xu, Jinchao; Liu, Chun Energetically stable discretizations for charge transport and electrokinetic models. (English) Zbl 1351.78040 J. Comput. Phys. 306, 1-18 (2016). MSC: 78M10 65M60 65M20 78A48 PDFBibTeX XMLCite \textit{M. S. Metti} et al., J. Comput. Phys. 306, 1--18 (2016; Zbl 1351.78040) Full Text: DOI arXiv
Hao, Wenrui; Xu, Zhiliang; Liu, Chun; Lin, Guang A fictitious domain method with a hybrid cell model for simulating motion of cells in fluid flow. (English) Zbl 1349.76472 J. Comput. Phys. 280, 345-362 (2015). MSC: 76M20 65M06 65M85 76Z05 92C35 PDFBibTeX XMLCite \textit{W. Hao} et al., J. Comput. Phys. 280, 345--362 (2015; Zbl 1349.76472) Full Text: DOI
Liu, Chun; Shen, Jie; Yang, Xiaofeng Decoupled energy stable schemes for a phase-field model of two-phase incompressible flows with variable density. (English) Zbl 1326.76064 J. Sci. Comput. 62, No. 2, 601-622 (2015). MSC: 76M10 65M60 65M70 76D05 76D27 76T99 PDFBibTeX XMLCite \textit{C. Liu} et al., J. Sci. Comput. 62, No. 2, 601--622 (2015; Zbl 1326.76064) Full Text: DOI
Wu, Hao; Xu, Xiang; Liu, Chun On the general Ericksen-Leslie system: Parodi’s relation, well-posedness and stability. (English) Zbl 1320.76010 Arch. Ration. Mech. Anal. 208, No. 1, 59-107 (2013). MSC: 76A15 35B35 35Q35 PDFBibTeX XMLCite \textit{H. Wu} et al., Arch. Ration. Mech. Anal. 208, No. 1, 59--107 (2013; Zbl 1320.76010) Full Text: DOI arXiv
Wu, Hao; Xu, Xiang; Liu, Chun Asymptotic behavior for a nematic liquid crystal model with different kinematic transport properties. (English) Zbl 1259.35040 Calc. Var. Partial Differ. Equ. 45, No. 3-4, 319-345 (2012). Reviewer: Junichi Aramaki (Saitama) MSC: 35B40 35B41 35Q35 76D05 76A15 PDFBibTeX XMLCite \textit{H. Wu} et al., Calc. Var. Partial Differ. Equ. 45, No. 3--4, 319--345 (2012; Zbl 1259.35040) Full Text: DOI arXiv
Hua, Jinsong; Lin, Ping; Liu, Chun; Wang, Qi Energy law preserving \(C^0\) finite element schemes for phase field models in two-phase flow computations. (English) Zbl 1408.76550 J. Comput. Phys. 230, No. 19, 7115-7131 (2011). MSC: 76T99 76M10 65M60 PDFBibTeX XMLCite \textit{J. Hua} et al., J. Comput. Phys. 230, No. 19, 7115--7131 (2011; Zbl 1408.76550) Full Text: DOI