Li, Rui; Gao, Yali; Chen, Zhangxin Adaptive discontinuous Galerkin finite element methods for the Allen-Cahn equation on polygonal meshes. (English) Zbl 07824757 Numer. Algorithms 95, No. 4, 1981-2014 (2024). MSC: 65-XX PDFBibTeX XMLCite \textit{R. Li} et al., Numer. Algorithms 95, No. 4, 1981--2014 (2024; Zbl 07824757) Full Text: DOI
Yan, Fengna; Cheng, Ziqiang Stability and error estimates of high order BDF-LDG discretizations for the Allen-Cahn equation. (English) Zbl 07800812 Comput. Math. Math. Phys. 63, No. 12, 2551-2571 (2023). MSC: 65M60 65M06 65N30 65M12 65M15 35Q35 PDFBibTeX XMLCite \textit{F. Yan} and \textit{Z. Cheng}, Comput. Math. Math. Phys. 63, No. 12, 2551--2571 (2023; Zbl 07800812) Full Text: DOI
Wang, Danxia; Li, Yanan; Jia, Hongen A two-grid finite element method for the Allen-Cahn equation with the logarithmic potential. (English) Zbl 07776961 Numer. Methods Partial Differ. Equations 39, No. 2, 1251-1265 (2023). MSC: 65-XX 35-XX PDFBibTeX XMLCite \textit{D. Wang} et al., Numer. Methods Partial Differ. Equations 39, No. 2, 1251--1265 (2023; Zbl 07776961) Full Text: DOI
Zhang, Danni; Guo, Ruihan Optimal error estimates of the semi-discrete local discontinuous Galerkin method and exponential time differencing schemes for the thin film epitaxy problem without slope selection. (English) Zbl 1524.65627 Adv. Appl. Math. Mech. 15, No. 3, 545-567 (2023). MSC: 65M60 35L75 65M06 65N30 65M15 76A20 35R09 35Q35 PDFBibTeX XMLCite \textit{D. Zhang} and \textit{R. Guo}, Adv. Appl. Math. Mech. 15, No. 3, 545--567 (2023; Zbl 1524.65627) Full Text: DOI
Zhou, Lingling; Guo, Ruihan Optimal error estimates of the local discontinuous Galerkin method and high-order time discretization scheme for the Swift-Hohenberg equation. (English) Zbl 1503.65254 J. Sci. Comput. 93, No. 2, Paper No. 46, 30 p. (2022). MSC: 65M60 65M06 65N30 65N35 65M15 65M12 35Q35 PDFBibTeX XMLCite \textit{L. Zhou} and \textit{R. Guo}, J. Sci. Comput. 93, No. 2, Paper No. 46, 30 p. (2022; Zbl 1503.65254) Full Text: DOI
Tang, Tao; Wu, Xu; Yang, Jiang Arbitrarily high order and fully discrete extrapolated RK-SAV/DG schemes for phase-field gradient flows. (English) Zbl 1497.65182 J. Sci. Comput. 93, No. 2, Paper No. 38, 23 p. (2022). MSC: 65M60 65L06 65N30 65N12 65N15 35Q35 PDFBibTeX XMLCite \textit{T. Tang} et al., J. Sci. Comput. 93, No. 2, Paper No. 38, 23 p. (2022; Zbl 1497.65182) Full Text: DOI
Ayub, Sana; Rauf, Abdul; Affan, Hira; Shah, Abdullah Comparison of different time discretization schemes for solving the Allen-Cahn equation. (English) Zbl 07565169 Int. J. Nonlinear Sci. Numer. Simul. 23, No. 3-4, 603-612 (2022). MSC: 65M60 65M22 65F10 PDFBibTeX XMLCite \textit{S. Ayub} et al., Int. J. Nonlinear Sci. Numer. Simul. 23, No. 3--4, 603--612 (2022; Zbl 07565169) Full Text: DOI
Wang, Jiangxing; Pan, Kejia; Yang, Xiaofeng Convergence analysis of the fully discrete hybridizable discontinuous Galerkin method for the Allen-Cahn equation based on the invariant energy quadratization approach. (English) Zbl 1490.65286 J. Sci. Comput. 91, No. 2, Paper No. 49, 23 p. (2022). MSC: 65N30 65N12 35K61 PDFBibTeX XMLCite \textit{J. Wang} et al., J. Sci. Comput. 91, No. 2, Paper No. 49, 23 p. (2022; Zbl 1490.65286) Full Text: DOI
Kim, Yunho; Lee, Dongsun Numerical investigation into the dependence of the Allen-Cahn equation on the free energy. (English) Zbl 1492.35338 Adv. Comput. Math. 48, No. 3, Paper No. 36, 32 p. (2022). MSC: 35Q82 35Q56 82B20 81V45 65M06 65M12 PDFBibTeX XMLCite \textit{Y. Kim} and \textit{D. Lee}, Adv. Comput. Math. 48, No. 3, Paper No. 36, 32 p. (2022; Zbl 1492.35338) Full Text: DOI
Hong, Qi; Gong, Yuezheng; Zhao, Jia; Wang, Qi Arbitrarily high order structure-preserving algorithms for the Allen-Cahn model with a nonlocal constraint. (English) Zbl 1501.65080 Appl. Numer. Math. 170, 321-339 (2021). MSC: 65M70 65L06 65P10 65M12 35K57 74A15 35Q74 PDFBibTeX XMLCite \textit{Q. Hong} et al., Appl. Numer. Math. 170, 321--339 (2021; Zbl 1501.65080) Full Text: DOI
Wang, Jiangxing Convergence analysis of an accurate and efficient method for nonlinear Maxwell’s equations. (English) Zbl 1476.65254 Discrete Contin. Dyn. Syst., Ser. B 26, No. 5, 2429-2440 (2021). MSC: 65M60 65M06 65N30 65M12 78A25 78M10 78M20 82D55 35Q60 PDFBibTeX XMLCite \textit{J. Wang}, Discrete Contin. Dyn. Syst., Ser. B 26, No. 5, 2429--2440 (2021; Zbl 1476.65254) Full Text: DOI
Yan, Fengna; Xu, Yan Stability analysis and error estimates of local discontinuous Galerkin methods with semi-implicit spectral deferred correction time-marching for the Allen-Cahn equation. (English) Zbl 1436.65145 J. Comput. Appl. Math. 376, Article ID 112857, 23 p. (2020). MSC: 65M60 65M70 65M12 65M15 35Q35 PDFBibTeX XMLCite \textit{F. Yan} and \textit{Y. Xu}, J. Comput. Appl. Math. 376, Article ID 112857, 23 p. (2020; Zbl 1436.65145) Full Text: DOI
Li, Can; Liu, Shuming Local discontinuous Galerkin scheme for space fractional Allen-Cahn equation. (English) Zbl 1463.65301 Commun. Appl. Math. Comput. 2, No. 1, 73-91 (2020). MSC: 65M60 35R11 65M12 65M15 35Q53 PDFBibTeX XMLCite \textit{C. Li} and \textit{S. Liu}, Commun. Appl. Math. Comput. 2, No. 1, 73--91 (2020; Zbl 1463.65301) Full Text: DOI
Guo, Ruihan; Xu, Yan Semi-implicit spectral deferred correction method based on the invariant energy quadratization approach for phase field problems. (English) Zbl 1473.65193 Commun. Comput. Phys. 26, No. 1, 87-113 (2019). MSC: 65M60 35L75 35G25 PDFBibTeX XMLCite \textit{R. Guo} and \textit{Y. Xu}, Commun. Comput. Phys. 26, No. 1, 87--113 (2019; Zbl 1473.65193) Full Text: DOI
Sun, Shouwen; Jing, Xiaobo; Wang, Qi Error estimates of energy stable numerical schemes for Allen-Cahn equations with nonlocal constraints. (English) Zbl 1502.65075 J. Sci. Comput. 79, No. 1, 593-623 (2019). MSC: 65M06 65M12 PDFBibTeX XMLCite \textit{S. Sun} et al., J. Sci. Comput. 79, No. 1, 593--623 (2019; Zbl 1502.65075) Full Text: DOI arXiv
Karasözen, Bülent; Uzunca, Murat; Sariaydin-Filibelioğlu, Ayşe; Yücel, Hamdullah Energy stable discontinuous Galerkin finite element method for the Allen-Cahn equation. (English) Zbl 1404.65173 Int. J. Comput. Methods 15, No. 3, Article ID 1850013, 26 p. (2018). MSC: 65M60 65M12 65M50 PDFBibTeX XMLCite \textit{B. Karasözen} et al., Int. J. Comput. Methods 15, No. 3, Article ID 1850013, 26 p. (2018; Zbl 1404.65173) Full Text: DOI arXiv
Uzunca, Murat; Karasözen, Bülent Energy stable model order reduction for the Allen-Cahn equation. (English) Zbl 1468.76042 Benner, Peter (ed.) et al., Model reduction of parametrized systems. Selected contributions based on the presentations at the MoRePaS conference, SISSA, Trieste, Italy, October 13–16, 2015. Cham: Springer. MS&A, Model. Simul. Appl. 17, 403-419 (2017). MSC: 76M10 76T99 76M30 65M12 65M15 PDFBibTeX XMLCite \textit{M. Uzunca} and \textit{B. Karasözen}, MS\&A, Model. Simul. Appl. 17, 403--419 (2017; Zbl 1468.76042) Full Text: DOI arXiv