Journal of Guangxi Normal University(Natural Science Edition) ›› 2025, Vol. 43 ›› Issue (2): 193-206.doi: 10.16088/j.issn.1001-6600.2024031701
• Mathematics and Statistics • Previous Articles Next Articles
WANG Zhaowei, WANG Danxia*
| [1] LI Y, AN R. Temporal error analysis of Euler semi-implicit scheme for the magnetohydrodynamics equations with variable density[J]. Applied Numerical Mathematics, 2021, 166: 146-167. DOI: 10.1016/j.apnum.2021.04.006. [2] CHEN Hang, HE Y Y, CHEN H T. Stability and temporal error estimate of scalar auxiliary variable schemes for the magnetohydrodynamics equations with variable density[J]. Numerical Methods for Partial Differential Equations, 2024, 40(1): e23067. DOI: 10.1002/num.23067. [3] 杨莉.求解Maxwell方程的间断有限元方法后处理技术研究[D].成都:电子科技大学,2022. DOI: 10.27005/d.cnki.gdzkn.2022.001713. [4] HE Y N. Unconditional convergence of the Euler semi-implicit scheme for the three-dimensional incompressible MHD equations[J]. IMA Journal of Numerical Analysis, 2015, 35(2): 767-801. DOI: 10.1093/imanum/dru015. [5] 胡凯伦, 陈敏, 罗宏. 磁流体方程全局吸引子的正则性[J].广西师范大学学报(自然科学版),2024,42(1):120-127. DOI: 10.16088/j.issn.1001-6600.2023032403. [6] 薛媛媛, 江珊. 带Navier边界条件的广义随机Navier-Stokes方程解的适定性[J].吉首大学学报(自然科学版), 2024,45(1):13-18. DOI: 10.13438/j.cnki.jdzk.2024.01.003. [7] 罗宏, 蒲志林, 周亚非.Navier-Stokes方程的渐近吸引子[J].广西师范大学学报(自然科学版),2009,27(2):38-41. DOI: 10.3969/j.issn.1001-6600.2009.02.010. [8] LI C Y, LI Y. Optimal L2 error analysis of first-order Euler linearized finite element scheme for the 2D magnetohydrodynamics system with variable density[J]. Computers and Mathematics with Applications, 2022, 128: 96-107. DOI: 10.1016/j.camwa.2022.10.013. [9] 毛静静. 变密度不可压缩Navier-Stokes方程的Gauge-Uzawa方法的误差估计[D].厦门:厦门大学,2019. [10] 申肖娟. 非定常不可压磁流体方程压力投影有限元方法的研究[D].焦作:河南理工大学,2020. [11] 刘盟. 向列相液晶流问题的能量稳定数值方法研究[D].太原:太原理工大学,2022. [12] PYO J H, SHEN J. Gauge-Uzawa methods for incompressible flows with variable density[J]. Journal of Computational Physics, 2007, 221(1):181-197. DOI: 10.1016/j.jcp.2006.06.013. [13] NOCHETTO R H, PYO J H. The Gauge-Uzawa finite element method. Part I: the Navier-Stokes equations[J]. SIAM Journal on Numerical Analysis, 2005, 43(3):1043-1068. DOI: 10.1137/040609756. [14] NOCHETTO R H, PYO J H. The Gauge-Uzawa finite element method. Part II: the Boussinesq equations[J]. Mathematical Models and Methods in Applied Sciences, 2006, 16(10): 1599-1626. DOI: 10.1142/S0218202506001649. [15] 张青. 非定常Magnetohydrodynamic方程的Gauge有限元方法[D].乌鲁木齐:新疆大学,2016. [16] GERBEAU J F, LE BRIS C, LELIE｀VRE T. Mathematical methods for the magnetohydrodynamics of liquid metals[J]. Oxford: Oxford University Press, 2006. DOI: 10.1093/acprof:oso/9780198566656.001.0001. [17] HECHT F. New development in FreeFem++[J]. Journal of Numerical Mathematics, 2012, 20(3/4): 251-266. DOI: 10.1515/jnum-2012-0013. |
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